Does cosmic zap need to be played the moment the user states he/she is using his/her power,
Strictly speaking, yes.
or can it be zapped at a more convenient moment?
Strictly speaking, no.
Also, can more than one colony be established in a deal, on any given side? Could two players just win on the first attack by declaring a trade of 5 colonies for 5 colonies?
Absolutely not. That's clear in the rules -- you can grant only one colony as part of a deal.