Rebecca, you're asking the right questions.
1. Hurricane season's over then, but it's usually windier. The whole Caribbean is good then,
beginning of the "dry" season. Bahamas probably a bit cold.
2.Liveaboards are great, but I would recommend to gain more experience before you go, to maximise the experience. Get an Advanced and Nitrox certification before you go.
The body can handle the 5 dives a day, especcially on Nitrox.
Nobody can predict the sea, but there is medication against seasickness.
3. You have Nekton and Agressor already, add
Dancer Fleet - Peter Hughes Diving for liveaboards.
Landbased you can look at Caradonna
Caradonna Dive Adventures - Dive Travel and Vacations, Maduro
Welcome to Maduro Travel, Inc., Undersea Adventures
Neal Watson's Undersea Adventures - Bahamas and Caribbean scuba diving resorts
4. Book airfare as soon as possible direct, agents usually don't get commissions anymore from the airlines, so you pay extra for the service. Only some still have good bulk contracts.
5. Grenada ( I have to say that)