The cruise ships dock in Charlotte Amalie. The shops are within walking distance.However, if you have difficulty walking, taxis are very accessible.

Blackbeard's Castle was not open due to Hurricane damage when we were there in August 2018. You could easily move around the area with no problem though.

We docked in Long Bay, I'm prob not the best person to answer, but Charlotte Amalie (where we did all our shopping) looks midway way between Crown Bay and Long Bay, and we walked there and back no probs. There were group taxi open air buses that charged $5 per person one way into town, so am sure that would be offered at your ship dock, I didn't see many private individual taxis at all.

You can take a taxi to the top easily. There are taxis available all around town. Bluebeards castle is higher than the steps as well as being several minutes away. However between the steps and the castle as well as spots lower than the castle are places where you can look out over the water and the view is quite lovely. The steps can be a little much is the day is really hot or you are a little tired if you are walking up but on the way down if you are not rushing it can be enjoyable, Feel free to stop to take pictures or even to rest a few minutes. Just remember this is your vacation so allow time to enjoy the view and make your special memories. Not every attraction is for everyone. Find yours and enjoy your time.

Yes you should have plenty of time.

I don't think it can be closed... per Torben above, it's public. However, many of sites (pirates tower, the rum distillery) appear to have fees involved. We were just walking so did'nt pursue. It's a nice invigerating walk and gives you a good sense of the city's layout from up there.

We were there this past October and were told that if you paid for the tour you could stay and swim

Check the website for the attraction/hotel. They will post days and times.

No the sky rides are across the street from Havensight (where cruise ships dock). 99 steps is in the middle of downtown Charlotte Amalie about a 5-7 minute car ride away from the sky ride.

Yes, you can climb the stairs and if you continue up the road you will find the castle and a beautiful view of the city and ocean.