I'm Italian and I'm trying to create an english name for a cultural club, whose mission is "seeking for knowledge together". I need a short, evocative, memorizable yet correct phrase, and I wonder if "QUEST IT" could satisfy all these requirements. Or if it is a nonsense for native english. Thanks for your help.
It sounds odd to me. You quest for things, or after things.
Perhaps you could call your club simply "Quest", so the name can embody both the noun and the verb, the search and to search.
not a teacher
Between "wrong, not appealing, archaic, adventurous, intriguing", I would have to choose "wrong", I'm afraid.
Having said that, the titles of companies and groups are frequently ungrammatical (Toys R Us, for example, would be very odd in normal English even if they had spelt "Are" correctly).
The simple answer is that you can call your group anything you like - it just depends on whether you want people to understand what the group is about simply from reading the name. If not, you can make it as unclear or intriguing as you like.