Never use god mode in any game. It sucks out all the fun. No exceptions.
Depends. I've played Fallout 3 and New Vegas before, gotten into mischief, been attacked and used God Mode, and then messed around with console commands on the enemies to see what silly stuff I can do.
It's not the point of using god mode so that you can just walk through the game, but rather using god mode so you can not worry about dying and then just piss around with whatever.
Is there an Online mode on it?
There is not, no. No multiplayer of any kind, local or online.