If you start at LGA you'll get both in that one day. The flight to FLL is the same plane that returns back to LGA.
Don't know about hotel, don't do priceline. Besides if you do as above you won't need hotel.
No, you can't get boarding pass for the return flight since the first leg hasn't departed. When you get into FLL just go to the gate and they'll give you your boarding pass along with a strange look (or maybe they've got use to this in/out by now).
At LGA, 55 may not be enougth time. Since the flight may come into one terminal and the outgoing is from another terminal, in this case you have to go out and go thru security again.
Best advice, if the flights are too close like at LGA, don't do it, book for a later flight and you can always standby the an earlier flight.
Take along a good book, some snacks, all you get is petz and drink, headset and cd or DVD to pass the time away. When we did the legs via MCO, one weekend the flight returned from MCO to MCO but next week the flight was going somewhere else and we arrived at a different terminal. Had plenty of time and we went on the standby list but did it at the ticket counter not the gate (our choice). LGA has a seperate ticket/checkin counters just for Florida flights. If you have any other questions just email.