For your resealing you will probably want to use Dicor sealant. This is the go-to for rubber roofs, but fairly certain they use the same for fiberglass pup tops. It is self-levelling, so no "wet finger" required if used sparingly. Never seen it in clear however (usually white, but I do see it in gray on amazon too).
Hard to say if this would work for a crack. Dicor probably flows a bit too much to do gap coverage, so if the crack is open much it may not work. You might want to use something more like an exterior butyl caulk for that if it is gapped?
I can't see any problem with sealing the wood on the underside of the floor. Both our Jayco's have had the wood coated with a black sealant from the factory. For the soft spot, you might want to consider gluing a cross brace in place for the length of the spot rather than setting up a jack each time, seems like a more permanent solution. If possible you could also attach it through a frame member with a bit of angle iron (bolted or/and welded).
IMO, carpeting would just hold the moisture underneath once wet. Gravel drains pretty quickly once the water abates. Many of us park outdoors year round and worry about water infiltration from snow and rain, but I've never really worried about standing water on the ground.
2011 Jayco X19H (purchased 2015)
2008 Jayco 1007 PUP (purchased new, traded for the X19)
2012 Chev Traverse LT with TP