Welcome to NorCal!
I'm assuming you mean Stillwater on the Sonoma coast (as I just learned, there is also a Stillwater in Monterey County). Based on that asssumption:
1) It takes me a little under 2 hours to drive to Stillwater from the Marina in SF if there is no traffic and my girlfriend is not in the car to yell at me for driving like a maniac on the curvy roads. With traffic or sensible driving, it's probably a little under 2 1/2 hours. I usually get off the 101 in Petaluma and, from that point on, it's a very pretty and enjoyable drive, so I don't mind the drive time at all. Probably add 30-45 minutes to either of those numbers if you're coming from San Mateo.
2) There are no full fledged dive shops close to Stillwater. The closest dive shop is probably in Bodega Bay. I believe you can get air-fills somewhere near Stillwater and I have seen tanks and well-worn looking gear for rent at the boat launch/campground up there, but I would recommend that you rent whatever you need before heading up. I just started working down in your neck of the woods (Foster City) and have had really good luck with the folks at
Wallins Dive Center.
3) Depends on when you're going. I've only camped at the campsites there twice and have not had any problem reserving like a week in advance. During peak times (like 3 day weekends, ab opener, nice summer weekends), you probably need to reserve months in advance. They have a few first-come-first-served spots, I think. There is no shortage of places to camp up there. If all the state park campsites are full, you're almost guaranteed to be able to find a spot at the less-scenic no-reservations-necessary private campground just a bit farther up highway 1 (can't recall the name at the moment, but you can't miss it).
Also, we have just formed a new dive club dedicated to diving the north coast (see website in my signature). Feel free to drop by our website or join us on one of our monthly dives! We are currently trying to have an official dive the first weekend of every month and someone seems to be planning to go diving most weekends.
--Scott