Your counter settings are useless because context stores only the environment plus content for the answers, nothing is done with them at this point. When you flush the answer blocks context sees them for the first time and the counter for the questions is 3 at this point and this is why you get always the same value.
\defineenumeration[exercici][text=Exercici]
\defineenumeration[resposta][text=Solucions]
\defineblock[resposta]
\hideblocks[resposta]
\starttext
\startexercici Question 1
\beginresposta
\resposta Answer 1 \par
\endresposta
\stopexercici
\startexercici Question 2
\beginresposta
\incrementcounter[resposta]
\endresposta
\stopexercici
\startexercici Question 3
\beginresposta
\resposta Answer 3 \par
\endresposta
\stopexercici
\subject{Answers}
\selectblocks[resposta]
\stoptext
Wolfgang