I tried the PS+ 14 Day Trial when i got my Vita, its about to run out today.

Will the games that are currently downloaded stop working all together when PS+ runs out, and will i only be able to "launch" them as soon as i resubcribe again?

You only get to keep the free games so long as you remain a PS+ member. Once your trial runs out, the free games you got will no longer work until you purchase them or renew your membership.

You can only play them while your PS+ subscription is active, yes.

Thanks!