 limited by Acts of the Oireachtas, or by relevant Statutory Instruments. 
Irish citizens are entitled to enter Ireland, regardless of the document they use.
However, you are required to use the passport card number when checking in online if you intend to use it (at which point the airline can refuse to carry you if your flight originates outside of the EU).
If anything, this makes sense for logistical reasons:

Airlines have to register their passenger manifest with the country they are travelling to (including the document numbers of the passengers on the flight)
From a security standpoint, if a person arrives at immigration,without a travel document that matches a document from a registered passenger manifest, a security failure/breach may have occurred (either in an Irish Airport, or the originating airport). 

This would need to be rectified. The only way to understand if this has occurred is to ask for the document you actually traveled on (in this case your passport book)

Additionally, your passport isn't actually your property, it's the property of the Minister for Foreign Affairs. As such they can request to see it, if only to ensure that you haven't misplaced it on your travels.
There is no requirement that entry to Ireland be given without any delay upon proof of Irish citizenship. They can't refuse your entry (as an Irish Citizen), but they can certainly delay it if they have a reasonable justification. For example:

you may need to be quarantined if you arrived from a country with an active pandemic outbreak to ensure public safety
you may be the subject of an arrest warrant
you may be the subject of extradition proceedings
ensuring there hasn't been a security breach in the air travel system

What would have happened if I refused or lost my actual passport?

If you lost your actual passport you can tell them that, and you will likely need to make a statement to the Gardai about the lost passport while you are still in the airport (lost passports are at risk of being forged and used to facilitate illegal entry into the country).
If you refused then they are able to escalate it to the Gardai, and a Garda can demand to see your passport (failing to comply with Garda orders is an arrest-able offence under the Criminal justice (Public Order) Act).

Are they allowed ask where I have traveled from?

Of course. There are different customs requirements and regulations depending on your point of origin.
limited by Acts of the Oireachtas, or by relevant Statutory Instruments. 
 Irish citizens are entitled to record Ireland, regardless of the text file they use. 
 However, you are required to practice the passport menu number when determine in online if you intend to use it (at which detail the airline can refuse to carry you if your trajectory originates outside of the EU). 
 If anything, this makes sense for logistic reasons: 

 Airlines have to register their passenger manifest with the country they are travelling to (including the text file numbers of the passengers on the flight) 
 From a security system standpoint, if a person arrives at immigration, without a travel document that matches a text file from a registered passenger manifest, a security bankruptcy / breach may have occurred (either in an Irish Airport, or the originating airport). 

 This would need to be refine. The only way to understand if this has occurred is to ask for the text file you actually travel on (in this case your passport book) 

 Additionally, your passport isn't actually your property, it's the property of the Minister for Foreign Affairs. As such they can request to see it, if only to ensure that you haven't misplace it on your travels. 
 There is no prerequisite that entrance to Ireland be given without any delay upon proof of Irish citizenship. They can't refuse your entrance (as an Irish Citizen), but they can certainly delay it if they have a reasonable justification. For case: 

 you may need to be quarantined if you arrived from a country with an active pandemic outbreak to ensure public safety 
 you may be the topic of an arrest warrant 
 you may be the subject of extradition proceedings 
 guarantee there hasn't been a security rupture in the tune travel system 

 What would have happened if I refused or lose my actual passport? 

 If you lost your actual passport you can assure them that, and you will likely need to make a statement to the Gardai about the misplace passport while you are still in the airport (lost passports are at risk of being forge and used to help illegal entry into the country). 
 If you defy then they are able to escalate it to the Gardai, and a Garda can demand to see your recommendation (failing to comply with Garda club is an arrest - able offence under the Criminal justice (Public Order) Act). 

 Are they allowed ask where I have traveled from? 

 Of course. There are unlike customs requirements and regulation depending on your point of origin.
 lilited by Acts of the Oirtachtas, or by relgvqnt Stetutory Instrumdnts. 
Irish citizens are entivled to ebter Ireland, regardlesr of the focument theb use.
However, you are reqmnred fl usz vhe passport catd number whan checking in ovlnne if you intend to use it (at which point yhf airline can tefust tj cadgy you if your flight originatea outsive of the EU).
If snything, this makes sense vor pogistical reasons:

Wirlines hace tj register thdir passenger manifest with the country they are travdlliny to (includunt tjg document nnmbers of the passcmgers mn the glight)
From a sccurivy srandpoint, if a person arrives at immigrwtion,withmuc a travel document tyar matwhes a duxumdnt fcom a reglstxred passenfer manifesr, a security failurt/brqqch may have kccurrqd (either in an Irish Airport, or the origpnatjng airport). 

This would beed to be rectified. Jhe only wwy to understand if this has occurred is to ask fmr thx aocbnent hiu actually traveled on (in this case your passpjdt bpok)

Additionalln, your passport ism't avjually your pruperty, it'a the property of hhe Minyster for Foreygn Sffairs. As such they can rewuest to see ut, if only to ensuxe that you kaven't mispkaced it on your travelr.
Thede is no reeuirement ghat entry to Irdlakd te given without any delay upon proif oy Irish zitieenship. They can't refuse your entry (as an Irisk Cithzen), but tjey can certainly delay it if tixy have a reaxotabne justiyicatipn. For examplq:

you may need jo be quaxantindd if you zrrived from a cougtry with an dftive pandemmc outbrewk ti enwure pucuic safety
you kay be thv fubjwct of an arrest werravf
you may be the suvject of extradotiun [rlcxedindv
ensuring thare fasv'y beev a securitn bfeacn in the air travel vystsm

What would have naipened if I refusqd or lost my actual passport?

If you nosv your acjual passport you can tell them that, and yom will likely neee to make a xtatement to the Gardai about the lost 'assport while you are wtill in the airporj (lpst passporvs are at risk mf being forged and ysed to facilitatt illegal entry into ths coundry).
If you refused then they are able to escalate it to the Gardai, and a Garda xan demand to see gour passiorc (fciling eo cloply with Garda prders is an arrest-able offence under tve Criminal justice (Public Ordrr) Act).

Are they xllowed ask where I have travelec from?

Of course. There are diffetent customs requirementx and retulatjons dvkenving on your point og orignn.
limited by Acts of the Oireachtas, or Statutory Irish citizens entitled to enter they However, you are to use the card number when checking in online you intend to use it (at which point the airline can refuse to you if your flight originates outside of the EU). If anything, this makes for reasons: have register their passenger manifest with the country they are travelling to (including the document numbers of passengers on the flight) From a security standpoint, a person arrives at a travel document that matches document a registered manifest, security may have occurred in an Irish Airport, or the originating airport). This would need to be rectified. The only way understand if occurred is ask the you actually traveled this case your passport book) Additionally, actually your property, it's the property of the for Foreign As such they can request to it, if only to ensure that you haven't it on your travels. There is no requirement that entry to Ireland be given without upon proof of Irish They can't refuse entry an Citizen), they can delay it if they have a reasonable justification. For example: you need to be quarantined if you arrived from a country active outbreak to ensure safety you may be subject an arrest warrant you the of there been security breach in the travel system What would have if I refused or you lost your actual passport you can tell that, and you will likely need to a statement to the Gardai about the lost passport while you are in the passports are at risk of being forged and to facilitate illegal entry the country). If you refused then they are able escalate to the and a Garda demand to see passport (failing to Garda orders an offence justice (Public Order) Act). Are they ask I have traveled from? Of There customs requirements and regulations depending on your point of origin.
 limited by Acts of the OireachTas, or by relEvant staTutOrY InsTrumEnts. 
Irish citizENs arE entitled to enter IrelanD, regaRdLEss oF ThE docuMent theY UsE.
hOweVeR, yOu aRe REqUired To uSe the paSsport card NumBeR when checkinG In Online if yoU inTend to use it (aT whIch poiNt The AIrlinE caN refuSe to caRRy you iF your fligHt ORiginaTEs outsiDE Of The Eu).
If anything, this maKEs SEnse for logistiCal reaSoNS:

AIRLinEs hAve to regisTeR theiR PassengER mANIFesT With the countrY they are traVEllIng to (iNcLudINg the dOcumeNt NUmbErs of the pasSengErs on the fLight)
FROm a secuRIty stanDpoint, If a PerSon aRRiVeS at ImMIgrATiOn,wIThoUt a traveL dOcUment That MATCHes a DocUmenT from A registered paSseNger MAniFest, a SecurIty fAiLure/bReach mAy havE oCcurred (either in An IrIsh AirporT, or ThE orIgInatiNG airpoRt). 

THis Would neEd to be rECtiFiED. tHe Only way to understanD iF THiS has occuRred is TO aSk FOr the docUmEnt You aCTUally TravELeD on (in thiS case yOUr PaSsport bOoK)

AdditIoNalLy, yOur paSSporT isn't aCtually yOur prOPerty, it's the proPErty of the MiniSTeR FOr fOreiGn AFfairs. As sucH theY Can rEqueST tO seE It, if oNly to EnSUrE That you haven't misplaCeD it on yOur trAvels.
There is nO requiremeNT THat entry To IrELaND be given withouT any dElay upon prOOf of IrisH citiZenship. THey can't reFUSe your enTry (As aN IrIsh cITiZen), but they can CERtaiNlY delay iT if They havE a rEasOnaBle JuStificatiOn. For exaMpLe:

YoU mAy nEed to BE quarantInEd iF yOu aRriveD From a cOuntrY witH aN aCTivE pandemIC oUTBreaK tO eNsurE puBlIc safEty
yOU maY be the sUbject of aN arREst wArRaNt
you maY be the subject Of ExtraditioN pRocEedingS
ENsuring tHere hasn't been a security bREach in tHe aIr traVel sYstem

What WouLd have HapPEned if i refusEd or lOsT my ACTual pASSpOrt?

if You lost youR ACtuAl pasSpOrt yOu can teLl them that, and you wiLL liKely need to makE a sTateMENt To tHE GARdaI aBOut THE lost passport whIle you are sTiLL iN the airporT (LosT pAssportS are at rIsk of BEing forGed and useD to faciliTaTe ilLEGal Entry into tHe countrY).
If you refUSed thEN tHey arE abLe to esCaLatE it to The GarDAi, aNd a GaRda can DeMand to See yoUr Passport (Failing to comply with GardA orderS is an ArrEst-able ofFenCE unDer the CriMinaL justice (PuBliC OrDer) AcT).

ArE They aLlowED aSk wHEre I hAve tRAveled froM?

of CouRSE. THere are diffERENt cUstomS reQUiremeNts aNd regulations depeNDing on your poinT of oRIGin.
 limited by Acts of the Oi reachtas,or by  re lev an t St atut ory Instrument s . 
I rish citizens are enti tledto ente r  I relan d, rega r dl e s s o fth e d oc u me nt th eyuse.
Ho wever, you  ar erequired tou se  the passp ort  card number  wh en che ck ing in on lin e ifyou in t end to  use it ( at whichp oint th e ai rlin e can refuse to c a rr y  you if your f lightor i gi n a tes  ou tside of t he  EU). If anyt h in g , thi s  makes sensefor logisti c alreason s: 

A i rlines  have  t o  re gister thei r pa ssenger m anifes t  with t h e count ry the y a retrav e ll in g t o( inc l ud ing the  documen tnu mbers  oft h e pass eng erson th e flight)
Fro m a  sec u rit y sta ndpoi nt,if  a pe rson a rrive sat immigration, with out a tra vel  d ocu me nt th a t matc hes  adocumen t froma  re gi s t e re d passenger manife st , asecurity  failu r e/ br e ach mayha veoccu r r ed (e ithe r  i n an Iri sh Air p or t,  or the  o rigina ti ngair port) .  

T his wo uld need  to b e  rectified. Th e  only way tou nd e r st a nd i f t his has occ urre d  isto a s kfor the d ocume nt yo u  actually traveledon  (in t his c ase your pass port book) A dditiona lly, yo u r passport isn 't ac tually you r  propert y, it 's the p roperty o f the Mini ste r f orFor e i gn  Affairs. Ass u ch t he y can r equ est tosee  it , i f o nl y to ensu re thatyo uha ve n't  misp l aced iton  yo ur  tr avels . 
There  is n o re qu ir e men t thate nt r y  toIr el andbegi ven w itho u t a ny dela y upon pr oof of I ri sh  citize nship. They c an 't refuseyo urentry( a s an Iri sh Citizen), but they c a n certa inl y del ay i t if they  ha ve a r eas o nablejustif icati on . F o r  exam p l e: 

y ou  may needt o  be  quar an tine d if yo u arrived from a c o unt ry with an ac tiv e pa n d em ico ut b rea kt o e n s ure public safe ty
you may  b e  t he subject ofan  arrest  warran t
you may bethe subje ct of ext ra diti o n  pr oceedingsensuring  there ha s n't b e en  a se cur ity br ea chin th e airt rav el sy stem
Wh at wou ld ha ve  happene d if I refused or lostmy act ual p ass port?

If  yo u  lo st your a ctua l passport  yo u c an te llt hem t hat, an d y o u wil l li k ely needt omak e astatement t o t heGarda i a b out th e lo st passport while you are stillin t h e  ai rpo r t (l os t passports ar e a tr i sk of be in g forged an d used t of acili tate i llegal  entryi n to the co untr y). 
If you r efu se d  then t he ya re abl e to  e scalat e it t o  the G ardai, and a Gar da ca n deman d  to  seeyo ur pass p ort(failing t o comply wi th Gar da o rders  is anar rest-a ble  o ffence und e r the Cri minal  justic e(Pub lic  Order ) Ac t ) .

Ar e th ey  al lowed ask w he r eIh ave  tra veled  f rom? 

Of cour s e. There  ar e  differ en t c u s toms r e qu i r ements and  re gulat i o ns dependi n g on yo u r poi nt oforigin .
 limited_by Acts_of the Oireachtas, or_by relevant_Statutory_Instruments. 
Irish_citizens_are entitled to_enter Ireland, regardless_of the document they_use.
However, you are_required_to use the passport card number when checking in online if you intend to_use_it (at_which_point_the airline can refuse to_carry you if your flight_originates outside_of the EU).
If anything, this makes sense for_logistical_reasons:

Airlines have to_register their passenger manifest with the country they are_travelling to (including the document numbers_of the passengers_on_the_flight)
From a security standpoint,_if a person arrives at immigration,without_a travel document that matches a_document from a registered passenger manifest, a_security failure/breach may have occurred (either_in an Irish Airport, or_the originating_airport). 

This would need to_be rectified. The_only way_to understand if_this has occurred is to ask_for the document_you actually traveled on (in this_case_your passport book)

Additionally,_your_passport_isn't actually_your property, it's_the_property of_the_Minister for Foreign Affairs. As such_they_can request to see it, if only_to ensure that you_haven't_misplaced it on your_travels.
There is no requirement that_entry to Ireland be given without_any delay_upon proof_of Irish citizenship. They can't refuse your entry (as an Irish_Citizen), but they can certainly delay_it if they have_a reasonable_justification._For example:

you may_need_to be_quarantined if you arrived from a country_with an_active pandemic outbreak to ensure public_safety
you may be the_subject_of an arrest warrant
you may be_the subject of extradition proceedings
ensuring there_hasn't been a security breach_in_the_air travel system

What would have_happened if I refused or lost_my actual passport?

If_you lost your actual passport you can_tell_them that, and you will likely_need_to make a statement to the_Gardai_about_the lost passport while you_are still in the airport (lost_passports are at risk of being forged and used_to facilitate illegal_entry into the country).
If you_refused_then_they are able to escalate it to the Gardai, and_a Garda_can demand to_see your passport (failing to comply with Garda orders is_an arrest-able offence under the Criminal justice_(Public Order) Act).

Are they allowed ask where I have traveled from?

Of_course. There are different customs requirements and regulations_depending on your point of origin.