What normally happens in these situations, once the new President takes office? I believe, in short term situations, they'd just keep things moving until the President was able to resume his duties.
However, when the handover is permanent, does the new President then select someone to be his VP? Or do they just reappoint the lower positions and carry on without a VP?
If they do pick a new VP, given that the official VP is usually the Presidents running mate, are there any restrictions on who they are permitted to pick?