1. Yes, you have 24 hours to leave the BVI after clearing out. Sometimes the C&I folks can be picky, for example when clearing out at 2pm and you tell them you are expecting to leave at noon the next day they might request (demand) that you come back tomorrow. So I usually tell them that I'm planning on leaving at sunrise (so before their office opens) but quite frequently I oversleep Yes, you may still go ashore after clearing out.
2a. Cruz Bay is still closed for customs and immigration, you need to go to Red Hook or to Charlotte Amalie I've just read that they are open and working from a trailer. When I went to the USVI from the BVI two months ago I was told that Cruz Bay was closed and I'd need to clear in on St. Thomas. I'd verify that they are open with someone who has done so recently.
2b. The boat doesn't have to be in the bay as C&I - but you are required to go ashore with crew to clear customs and immigration immediately upon arrival, and dropping the hook or picking up a mooring counts as arrival. So you would need to be able to justify the added distance and prove timing if you are asked.
3. I don't know about Red Hook, but you can tie up to the shoreline dock close to the Charlotte Amalie office (which is in the ferry terminal building on the ground floor in the back)
4. No seal, but your holding tanks should be closed.
5. See 2a, but yes - a $5 taxi ride from all of the protected anchorages to the north will bring you into town
6. The restaurants have changed since the hurricanes so I can't help there.

Addendum: Everyone aboard must be either a U.S. Citizen, LPR, or have a tourist or similar visa for the USA, that means any Europeans aboard who are used to flying with an ESTA will not be able to travel to the USVI via sailboat. They can always take the ferry, the ESTA works for that. The good news is that when you return to the BVI you don't have to clear out.