For push-ups, I use a set of things called Perfect Push-up that relieve the strain on my old arthritic wrists. They also let you go a bit deeper. You can find them on Amazon and there are probably similar products.
I have a doorway pull-up bar, but I wish I had something wider. It’s fine for normal exercise, but I can’t get very wide.
I do chair dips, but I’d really like to get a proper dip setup someday. That would be much more comfortable and gives a better exercise. I just don’t have any good place to put it right now.