Oliver came through the surgery well - his heart and blood pressure remained at healthy levels the whole time. The anal gland problem turned out to be fistulas rather than abscesses, though fistulas can originate from chronic anal gland infections when the glands are not removed. (Unfortunately, Oliver's previous vet advised his mom against the anal gland removal, a procedure which is usually recommended when a dog has more than three episodes of infected glands in a year.) I won't get into the gory details of fistulas, but for those who want to know more, this link is a good resource.
Oliver did have some small tumours which have been sent to pathology along with the enlarged testicle - it will be a few days before we get those results back. Meanwhile, our paws and fingers and toes will all be crossed, hoping everything is benign.
While one vet worked on the back end, another worked on the front end. Oliver lost a lot of teeth, which I rather anticipated. It'll be mushy food for a while for the little guy.
Oliver is staying overnight at the vets, as he is still very groggy and they are keeping him on fluids as long as possible. Hopefully, he will be ready to come home in the morning. Sleep well, Oliver - in a few days you'll feel so much better and be terrorizing the cat once again.
Thanks, everyone, for your many prayers and healing thoughts.