Hi David, without seeing the situation first hand it's difficult to offer advice, but in general terms, here goes.
can be rebuilt if you feel so inclined and know how to do it and can get the necessary parts. The advantage is that replacing the entire axle
means no old parts that may fail later and it's likely to be properly assembled. Installing a complete axle may be easier and less work than rebuilding the original. The last time I had to do this I priced both options and a new axle cost less than the parts for a rebuild although this may not always be the case.
Soft floors are a common problem with lightweight trailers as thinner materials are used to reduce weight
. I've seen full and partial floor replacement from above and beneath the unit. It depends on what you have work with and how extensive a repair you want to make. An off frame full floor replacement is certainly the best option but it is a lot of work and you will need a place to do the work plus necessary tools and equipment.
If the frame and supports under the floor are in good shape and your floor is just a little spongy, I would put a layer of new plywood over the existing floor. Half inch plywood would be a minimum but 5/8 would be even better. As you go thicker the weight
of the plywood is a trade off between strength and weight
Some Pics may help. Good luck with your project!