This is a closed cell type of foam that is impermeable, so can insulate a space without a poly barrier.The foam does such a good job of tightly sealing hard to reach areas and the underside of plywood where you want to avoid a cold floor.

I work in commercial construction and for balconies (which would be a similar condition) we use a traffic coating (water proofing) over the top of the concrete and a drip edge on the perimeter at the underside of the balcony to prevent water from rolling back in.

I am looking at a house from 1957 that has lead paint on the exterior that is under siding. 

A quick test for sagging joists is to put a nail on the underside of the joist on each end and then tie off a Mason line about an inch down.

Paint all wood with Killz primer to seal it, might even need to paint underside of roof.

If this were a problem with vapor barriers on the under side of the floor, could there possibly be enough moisture coming from the seemingly dry crawl space to create extreme humidity inside the house? 

The squeaks drive me nuts, I can't get to the underside without taking down the ceiling in the basement.

I would paint that underside of the house in the parking area.

Having been in a few crawl spaces with water, if the water has been there constantly, there might be mold on the underside of your flooring, which could be a problem. 

It is these properties which make moss not only very very good at reproducing on your roof, but also make it so damaging.The Rhizomes of Moss burrow into and bond with the granular surface of the roof and can and will penetrate the underside of the leading edge of the shingles on a roof.