Hi so what happens if, like just now 2v2, I join a laggy game? Is there any way I can quit without losing points?
After about 10 minutes one guy left and the connection was considerably better. Before I had a lag of about 5-7 seconds.
What happens if the host quits in a rated game?

You could try to save & exit at the start of the game, but otherwise the best method would be to use the command before the game room launches as this will let you see the pings of all the players connected to you. Anything over 400ms might be problematic, and so you can avoid starting the game when those scenarios happen since lag is likely to occur.