Yes, generally they are removed when they expire. In detail it works like that:
If a gallery is not used (visited) for 3 months:
1. its owner receives a warning email, so that she can extend the expiration by another 3 months
2. if the expiration isn't extended within 1 month, the gallery is marked as expired and becomes inavailable for visitors
3. the owner may still be able to see the gallery in the Trash folder (in the control panel of JB) and un-delete it.
4. after some time the gallery disappears completely and even its owner can't see it in the Trash folder
If you have a Premium (paid) account, all of this never happens - it's like as if the gallery was active all the time, so it just doesn't expire.
As for payments, they are processed by Fastspring and they do make invoices.
ps. To sum up: remember that galleries expire only when they're not used (visited).
As long as they are used in some auction, their expiration date is automatically extended.
If they are not used, you can still extend them manually.
But if you do nothing, then they will be removed.