In tournaments with teams, if a player is getting timed out of their games, does that team will probably have to resign itself to losing all of its remaining games, or can players resign?  If the latter, do all remaining games count as losses?

a. in the tournament (I'm pretty sure, yes)

b. in their personal stats?

If one of your teammates quits then you are pretty much doomed as a team. This affects your tournament team stats only.

What if you quit from a tournament? All are counted as loses for you and your teammates?

Well basically you're teammates are screwed - they can either try and win each game man down or quit themselves.

I know this has been said before, but I'll mention it again. It would be nice to invite/reserve seats in team games.

I was looking forward to the Triumvirate Inagural tourney until a teammate got the boot after 2 turns. When I joined I PM'd people to join the team I made, but they didn't get there in time.