Can an overbite cause facial asymmetry?

Yes especially if only on one side or more on one side or the other. Dentist can help answer.

Yes

It's more probable that whatever dento-facial imbalance is causing your overbite is also causing your facial asymmetry. Please see an overbite/facial asymmetry expert, a specialist Orthodontist, for an Initial Examination (usually complimentary). Your problems fall right into an Orthodontist's wheelhouse.