When someone joins, they get their own private link — that's the only place their assignment ever shows up. There's no public list of who has who; each person can only ever see their own match.

Everyone is shuffled into a random order, then each person is matched with whoever comes right after them in that shuffle (wrapping the last person back to the first). This guarantees nobody is ever assigned to buy for themselves.

Yes — anyone who's joined can be removed from your dashboard right up until you draw names. Once names are drawn, the participant list is locked.

At least 3 — with only 1 or 2 people there's no meaningful way to keep a gift exchange secret.

Yes — just create a new event whenever you're ready to run another one. Each event and its join link are completely independent.