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Yes. You can only team up with other people that chose an option allowing them to team up.

Do both people die at the same time if they are on a team, or is there a way for 1 person to survive?

Depends on the choices available. Last season lots of teams were broken up by single deaths, and new teams formed again later.

For a better understanding of how that works, I would recommend going back and reading through the game posts of Season 4 if you have the time to do so.

I'll do that, thanks!