My senior unneutered dog has prostate tumors. Should he be castrated?

Poor Alf! Studies have shown that neutering does not provide any protective effects against prostate cancer in dogs - in fact, neutered males have a slightly higher incidence of this disease than intact males. So I'm not quite sure about the reasoning for having him castrated, unless what your veterinarian meant was that Alf has prostatic cysts or benign prostatic enlargement - both of these things would be expected to improve with neutering.

It would help to know exactly what diagnostics have been done and what the results were in order to give more specific advice - feel free to request a consultation with one of us if you want to upload copies of his lab reports and medical records for us to look at. Otherwise, if you're unsure about your current vet's recommendations, I would suggest going to another local vet for a second opinion, or requesting referral to a specialist for further evaluation.