There are no air fills available at Dry Tortugas. The Park Service has a compressor, but it is not for public use. You might talk one of the dive boats there into giving you fills, but it isn't likely. The three boats that are routinely there are Spree (mine, not likely), Ultimate Getaway, and Playmate.
The anchorage is public, first come, first served. I don't go into the inner harbor to anchor, too much risk of the wind shifting at night and me swinging around and taking out other boats. I anchor outside near the fort. Anchoring is only allowed within 1 mile of the fort at night, and never in the Research Natural Area. The dock sits 6 feet off the water and is available for a maximum of 2 hours between sunrise and sunset. Basically for you to offload your camping gear. Then you go back on the hook. You may not use the dock when the ferry is there.
There are 4 buoys in the park for diving, only 3 were installed when I was there last. The park ranger can give you the numbers, but they are at Texas Rock, Offramp, and 2 others. There are 13 buoys up in the North Ecological Reserve of the Florida Keys National Marine Sanctuary. There is no anchoring in the North Ecological Reserve. The buoys that are up are listed on their website. They change seasonally, so your info is better gleaned there than from me.
Spearfishing is not allowed in the Dry Tortugas National Park at any time ever don't even think about it. Spearing is not allowed in the Florida Keys National Marine Sanctuary Tortugas Ecological Reserve ever either. You may not even enter the Florida Keys National Marine Sanctuary South Ecological Reserve. No anchoring in any of those places. No hook and line in the North or South Ecological Reserve. There is damn fine fishing, however, along the boundaries. I'd get a really good GPS and sounder and when you come across bottom, make sure you are out of the closed area and have a ball. The area is patrolled by USCG, NOAA, FWC, and NPS all of whom will board you, check the tracklines on your GPS, and write big-ass tickets if they find you fishing illegally, even if fishing illegally wasn't your intent. To enter the North Reserve, you must obtain a permit, which can be done by calling the Sanctuary office at 305-292-0311. The receptionist is Carla and ask her for a TER-N permit. When you enter the park with speared fish, your guns must be broken down and stowed, and you have to call the park ranger and tell them what you have onboard. Do not screw this up. They don't know where you've been and if they find you have unstowed guns, you will receive a ticket. It's a federal ticket, and the fines can be awesome. The rangers have no sense of humor, and "I didn't know" is not acceptable.
My wife tells me that you must have an appointment and permission to camp on Garden Key. Summertime camping permits are very restricted due to the number of applicants. If you can stay on the boat, you are golden. No pooing in the harbor, you gotta have a MSD.