Re: neighbors trees and hard pan
You have the right to prune any neighbors bushes, shrubs, and trees that encroach on your yard. The fence is the property line and you can cut anything that hangs over it. If the neighbor is unwilling to deal with the tree, then it might be time to give him back the leaves from his tree. Instead of bagging them up, toss them back over into his yard, preferably after he's just raked his side up.
The bad soil on your side will be fun to deal with. If you can't get a shovel into it when it's wet and moist, then breaking it up to get organic matter worked into it will be a chore. If there's enough room to fit a rototiller, that will be the easiest way to do the work. The cure for the bad soil will be to work organic material such as manure or compost as deeply as possible.
Another alternative to improving the soil would be to plant in containers and landscape with pavers and/or decorative gravel.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!