Can general anesthesia, vicodin or naproxen affect birth control? (mini pill)

They shouldn't. None of those should interfere with the minipill. However, the minipill is a Progesterone only pill and tends to be pretty sensitive. You have to take it at the same time every day and stress can effect it. If you are worried, use a back up method like condoms for a couple of days.
No. The medications used should have no effect on the actions of the mini-pill.
Probably not. Ther is no evidence indicating that anesthesia or the medications you have listed would interfere with birth control pills.