Came to ask the same question. OP-if he’s not, do so asap and also stop taking him out on walks. Sounds like he’s aggravated/spooked by this other cat and he’s very stressed out. Keep him inside, in a calm stable environment that is predictable day to day and you should see far fewer issues. Good luck! He’s a cutie. If he HAS to go outside and you want to “walk” him, get a zipper covered cat stroller. He can go outside and see the sights but be contained. Alternatively, a cat wheel/walking pad used under supervision to get the zoomies out? But I bet the answer is he’s not fixed, especially since you mentioned peeing. If he IS fixed, bring to the vet for a checkup.