Quest completing

Is it posible to see which quest you have completed? and when yes which button do you need to press to see that?

nopey

Unfortunately no. It would be a great feature for Anet to add, another tab on the quest log showing which ones have been completed.

Guildwiki has lists by chapter so you can at least check them out and perhaps visit the quest-giver to see if they have a quest for you.