What happens to all your active games? do you get booted or what? How long is the time period?

You aren't able to log into that account. You might be given a time period similar to coming back from vacation to surrender in all of your games, if not then the game just waits until you haven't taken your turn in a quick enough amount of time and boots you.
I know because I was in one of Sun God's games when he got banned and he surrendered and said that he wouldn't be able to play any games for a while.

ok thanks, I was planning on banning myself, maybe I'll do it later or something.

O.o

You get redirected to Warlight.net/banned and then it tells you you're banned, for how long, and the reason why you were banned, usually with a transcript of what you said to get banned.

Keks were had

Funny that some people think you can get banned if you :

1. Refuse to vote to end a game.
2. If you boot someone.
3. If you win by a large margin and the player cant figure out why.
( I have the perfect moves in this game and there is no way you could have beaten me).
4. If you return after being booted and win the game.
5. If you make an alliance with another player.
6. If you say something in the lobby that isn't true.
( like, " I have 230 income so you should surrender" but you really have 12)

I am sure there are others too.