Pence probably would. Even a Democratic successor might (for some crimes) just because it's more politically expedient than dealing with what would, arguably, be a political prisoner if he were convicted and imprisoned. Again, depending on the nature of the charges.

He probably could. I don't think there's anything that prevents a successfully impeached person from holding office again. It just removes them from office and requires reappointment or reelection. But I think he'd lose the popular vote again and probably the EC since enough people would've finally wised up (or just lost the momentum).