When a member is banned from a group, is that ban connected to their email address or their personal information?

To their email address. However, apparently there is another kind of banishment (available only for paid groups, as far as I know).
At this point, I'll leave it to be further discussed as I can't remember right now the necessary info to give you about it.

Cheers,
AKA Starboy

Sent from a galaxy far, far away.