Most of your questions have been answered except for use of resort facilities. Leverick is very causal about the use of their pool and facilities. I believe that is also the case at Scrub if you are docking with them.
Bitter End charges for use of their pool and facilities. If you dock at Peter, you may be able to use the pool, but, in general, Peter is not friendly to non-guests.
The Anegada Beach a Club is very friendly about use of their facilities. Not so much at Little Dix (unless you are going to their spa,) Biras and Oil Nut Bay. You need to be a guest at Guana.
I am less familiar with the resorts on Tortola.
Everywhere else, the spectacular beaches are wide open for your use.