Your naming of the fragments looks OK, though I don't understand where you're getting 2-butanoate from (3-butanoate?). You're not putting the fragments together correctly.
Ethyl butanoate is your parent fragment.
Think about this and try again:
EtCOOEt = ethyl propanoate
CH2(OH)COOEt = Ethyl 2-hydroxypropanoate [note: not (ethyl 2-propanoate) 2-hydroxide]
similarly:
EtCOO(CH2)4COOMe is called Methyl (5-propionyloxy)pentanoate
ie. the substituent is named with an "oxy" suffix, not named as the anion - hydroxy not hydroxide, propionyloxy not propionate, acetoxy (aka ethanoyloxy) not acetate (aka ethanoate).
Does that make sense?