are there places to stay:
yes see
http://www.cuttyhunk.com/ and
http://www.cuttyhunkfishingclub.com/
can you reserve moorings/dock space :
There are moorings I think they are $25/night. See the dockmaster. You can anchor in the outer harbor but if it blows NE you have a problem. I would rec stay in the inner harbor. Lots of sail boats make a stop there.
does the island have gas? They did when I was there.
where to fish/tactics? The place is a bass meca. Head to any rip and submerge some live bait OR troll around the place until you catch your limit. You should not have a problem. Head to Pigs/Sows for a sure thing.
When boat fishing close to shore: WARNING: WATCH OUT FOR ROCKS. This place is land-mined like few others and currents can be very strong here.
Any other suggestions : BYOBooze and BYOBait. There is no real tackle store to speak of and the place is dry. That said, it is a big fishing and drinking island....go figure.
Camping: I don't think so unless your on private property and have the owners permission there is no campground.