Welcome from up here in Gainesville.
The January hang that zukiguy mentioned has a planning thread located here, and a sign-up sheet located here.
To answer your questions from the perspective of someone who's been bike camping for a while and only hiking for the last six months or so...
1.) Buy the gear first, unless you intend on getting something modular like a Molly Mac Pack that scales in size from a day pack to considerably more volume. That way, you'll have an idea of how much volume you're going to need. (A note: personally, I find that the majority of major pack makers overestimate the amount of gear one needs--what they consider a day-and-an-half pack, I can usually get three to five days out of in the field under normal Florida weather conditions.)
2.) There are a number of very nice integrated bug net designs out there. However, any single-layer hammock is going to leave you vulnerable to bites through the bottom. I personally recommend using a Permethrin treatment on the hammock (available at most outdoor stores) to keep the buggers off of one. Or, you can go the double-layer route or even get a hammock with a 360* bug net that completely encloses the hammock. There are a myriad of designs, most of which have design points that are argued over (politely) and dissected here on Hammock Forums. Here, making it to the Ocala hang would probably be your best bet. If you can't, though, don't despair: hiking weather is here to stay through March-ish, and it's very likely that there'll be several other hangs in Florida between now and then.
3.) You most definitely can. The trick, from what I've read here (and my experiences with my poncho liner underquilt bear this out) is that the hammock wraps around your shoulders and hips. You'll either want a very wide pad or pads, wide enough and thin enough to wrap with the hammock, or you'll want to do something called an SPE. An SPE is a Speer Pad Extender (unfortunately no longer commercially made), a nylon bag that holds your pad and smaller pieces of other pads in the critical areas around your torso and hips to ensure that you don't get cold on your sides.
Honestly, though, I like my PLUQ. It's gotten me down to 39 so far, though I was a little chilly. Which covers 90% of the weather you're likely to run across in south Florida.
Anyway, welcome to the forums!