Can I react a Grignard reagent (ethylmagnesium bromide) with water and then ammonia?
I came across this question where I had to convert
  $\ce{CH3-CH2-Mg-Br}$ to $\ce{CH3-CH2-NH2}$. If I need to do so can I
  just react the given compound with water [...]


Always be cautious about unwanted, side reactions that may occur. Proton exchanges are one huge class of possible side reactions. Protons transfers occur readily in many circumstances because the protons is small and can be shuffled around without much to get in its way, physically. 

So in the case of your hypothetical reaction between a Grignard reagent and water - realize that Grignards are strongly basic and therefore will deprotonate water. Unfortunately protonated Grignards are no good in terms of reactivity. They just fall back apart into hydrocarbons and a basic halide salt. 

Further reading regarding Grignards - It is tempting to use Grignards to create carbon-carbon bonds, but anything that is acidic as water or more acidic will be deprotonated by the Grignard before any carbon-carbon bonds are created. When preparing Grignards, glassware must be perfectly dry. Not just wiped dry with a paper towel but heated dry. Grignards also live in ether solvents since ethers are only very weakly acidic. 

Grignards may be used to attack aldehydes and ketones in creating carbon-carbon bonds, but realize that if the aldehyde or ketone contains a functional group that is about as acidic as water or more so - then the first equivalent of Grignard you add isn't going to the aldehyde or ketone carbon - it's going to perform a proton-transfer. 


  Is there any set of principles in organic chemistry which govern as to
  which substances can be replaced with what?


In general, it is good to keep in mind the motif nucleophile attacks electrophile in introductory organic chemistry. 

Exceptions to motif: nucleophile attacks electrophile

Other heuristics you can use in predicting what reactions might commence ... 


Bond energies. This is mainly useful for studying radical reactions - to which the motif nucleophile attacks electrophile doesn't apply as well. Are we going from weaker to stronger bonds? That's a favorable move, enthalpically. 
Polarities. This falls under nucleophile attacks electrophile. 
Kinetics. It's good to learn the difference between thermodynamics and kinetics early in organic chemistry. Sometimes chemical entities may be thermodynamically unstable but kinetically stable. Maybe a carbon is particularly electrophilic, but it's too well "hidden" by neighboring groups (steric hindrance). So will a nucleophile attack this carbon? Probably not to a great extent.