Thank you all for your thoughts and suggestions.
My male neutered cat’s behavior is always changing. I picked him at the SPCA because no one wanted him. He was very squirrelly, hyper, nervous and shy. For the first month that I had him he would spend his days in hiding. I spent many hours playing with him. But he would quickly retreat back into hiding. Day after day I saw very little progress. Only after many months he started acting less and less afraid. I’ve never gotten him to purr (maybe someday).
Nowadays he is like Jekyll and Hyde. He can be very outgoing seeking affection from my wife and I (including snuggling) and even aggressive playing to our other male cat (never showed aggression to me or my wife). On other days he’s timid and runs away for no apparent reason. He can be so sweet and so cute. It’s the way he looks at you with those adorable wide open round eyes. Somewhat like a teddy bear.
He’s using his cat box regularly now but if I move his cat box just a foot or two away from the normal location then he will start pooping in the planters and peeing wherever he pleases.
I don’t think that he vomits any more than any normal healthy cat vomits.
He’s also very finicky about his food. He’ll only eat a couple types of food.
I take him to the vet once a year for a check up and shots.
Oh about having cats in the bedroom at night. My wife says no. But a couple of times the cats have snuck in an hid under the bed. Then when we were asleep they start climbing all over the bed so much that we can’t sleep. Scratched up the wood parts pretty good. If they would just be still and sleep then I’d let them in.
So for now I sleep well until the door banging starts at around 2 am. Then I go down stairs to sleep on the couch with the cats.