Is this a thing for solo developers only? I have a group of 3 people (so far) who are hoping to start making a name for ourselves by doing game jams. Would we be allowed to submit a game as a group? And if so, how big can the group be?

Short answer: Yes You can form a team. There is no maximum team size, so go nuts! When submitting, one member will make a new game page here on Itch. Then, they will add all of their teammates as admins on the game. Doing this ensures that all teammates will be able to rate other submissions.