Upgrading apartment: GFCI/AFCI breakers and wires
AFCI vs GFCI

You're using AFCI/GFCI interchangeably like they're "Thing 1 I don't know what is", and "thing 2 I don't know what is".  Actually, they are not similar. 


AFCI protects wiring in the wall from starting fires (and to a far lesser extent, appliance cords).  That may or may not be warranted depending on your wiring, and the scope of your permit/work.
GFCI protects humans from shock.  It needs to protect appliances that plug in anywhere water could be found, and wires that might get wet. 


If you saw all the flooding in Houston where the first floor of buildings was flooded out and people were on the 2nd floor with the power on and A/C running, that's because the overhead service drop and panel are on the 2nd floor, and all the 1st floor circuits are on GFCI (and tripped obviously).  Because those places were built to flood. 

Scope of AFCI/GFCI

Now in NYC it's common for them to require metal conduit (typically EMT) for all wiring.  Metal conduit is not the use-case for AFCI. Code recognizes this to a limited degree; normally AFCI must be at the service panel, but if it's metal conduit, the AFCI protection can be at the first outlet.  ACFI receps are half the price, probably because there's more room in a recep; flipside is AFCI receps are huge, and that can sometimes be a problem with metal boxes.

Any AFCI device has LOAD terminals and it can protect any downline wiring (and outlets) connected to those LOAD terminals.  Since 90% of the goal of AFCI is to protect wiring, you need to do that, or it would defeat the entire purpose!  If AFCI is mandatory, that is mandatory.  (What NOT to do: have an AFCI recep at every recep outlet). 

GFCI devices also have that LOAD feature.  However lots of people don't use it, and that's fine unless the wires themselves have a chance of being flooded or subject to groundwater action (e.g. wiring to a boat dock).  But hey, the feature is free. 

Since you are wiring a kitchen, really make a point to have the refrigerator be not on a GFCI or AFCI if avoidable.  Refrigerators are simply not a use-case for GFCI devices.  As far as AFCI, they contribute little when the refrigerator recep is wired in metal conduit. 

Questions


  Upgrading the current breaker with AFCI/GFCI breaker is the way to go, correct? I don't see a reason to not upgrade it. Is there a situation where it is not recommended?


Refrigerators and other safety equipment.  Keep in mind these are safety devices (fault detectors) and they will trip if a fault is present.  That seems better now, but it will seem worse when they start tripping due to a fault. 


  Is there any recent technology I should consider during this upgrade? I read a little about smart power monitor that is installed in the breaker.


Whole house surge suppressors will become Code when your locality adopts NEC 2020.  The simplest occupy 2 spaces in the panel, except that being in NYC you will probably need the far rarer 3-phase unit which takes 3 spaces.  Electrical upgrades take a lot of spaces.  Get a huge panel to suit - 42 spaces is NOT excessive. 


  Considering the breakers will be converted to dual (GFCI + AFCI) protection, would it be OK to leave one or two GFCI/AFCI outlets in place, or it is recommended to replace them with regular outlets since breaker will already be GFCI/AFCI?


Don't need them. They will be redundant to the point of annoyance - you will need to reset them in a particular sequence. 


  My conduits are narrow (old). I rewired two places already. A solid wire is very hard to pass. A stranded is much easier. Would it be OK to use stranded in the whole apartment (living, kitchen, bath, etc.)?


99% of my work is in conduit. Solid is a nightmare. I own only stranded #12 wire and I use it for all 15-20A circuits. However, stranded is not allowed in backstabs, and attaching it to screw terminals without it birdcaging is a fine art.  Best to either get the $3 screw-to-clamp receps, or pigtail your receps and switches with bits of solid wire (which I gather you have plenty of). 


  I will try to organize the breakers. Currently there is one breaker switching off lights and outlets in different (nearby) areas, I'd like to separate to have better control. 


Try to have the lights and receps for a given room be on different circuits.  That way you aren't plunged into the dark when a breaker trips. 


  If I want to create new outlets in the bathroom (small bathroom), what would be the recommended procedure: break the wall and use NM-B cable? break the wall and install conduit? not break the wall and just use a wire cover with a waterproof cable like NM-B? 


NM-B is not waterproof (where did you get that idea!?) It fails quickly when wet.  Whether you are allowed to use cable wiring methods is decided by your local Electrical Codes.  

Rule of thumb: If all the wiring in the facility is in conduit, Code requires that. People don't put in conduit for their health. 


  Looking up online, I only find THHN stranded. I could not find THWN stranded wires. Why? 


95% of the THHN wire out there is cross-listed both THHN and THWN-2, and meets both standards at the same time.