Umm.. I don't think you can neuter with kidney issues, depending on the severity of them. The anaesthetic is particularly hard on the kidneys, so it might be a huge risk.
Intact dogs mark a lot when they're older and especially if they're dominant. Neutering won't help that at this point either, but house training like Lucky suggested might help.
Personally, I'd get a check up at my own vet before really assessing how the doggy is. Sometimes, some shelters don't have enough time to thoroughly check the dogs, and I trust my vet more anyway.