Is it possible to have a chess game in which each player has 45 minutes time, or longer.. in the site chess.com of course .

Yes, choose "Custom" and set it to whatever you want.

I haven't joined it, but the group "Dan Heisman learning center" supposedly has mostly members who prefer longer time controls.  Might be worth checking out...

In live chess, in online chess the minimum time is 1 move per day.