Its a good idea to keep the kitten (who is adorable) in a seperate room from your other cat for 7-10 days to prevent infecting your older cat. It can take that long for a cold to show up in the kitten, and you don't want to have to treat the new and old with medication if you can avoid it.
You also do not want to place the kitten i a place of importance to your other cat. Like if the best place to sleep at night is your bedroom. Then isolating the kitten in the bedroom would be a bad idea. As your ranking cat could become agitated about that.
There is a good chance the cat will only use the potty when you are not there as he is frightened in his new situation. Its normal. We got 3 new cats this year, all different ages, and all potty trained when we got them at 3.5 yrs, 1 yr, and 15 weeks.
They all take different amount of times to socialize. Its a good idea to just let the cats meet under the door for now. After the medical clear has occured. You can swap bedding, swap towels they may be sleeping on, swap litter boxes... so the cats get use to each others smell. The other thing that works great. Rub a towel on the cats side, and side of face (there are scent glands there) then rub it on the other cat, the back to the original cat. Cats def do not like it, but it gets the cats with a common scent faster.
Do that for a couple times a day, for a good week, helps things calm down faster.
One other thing you can do. When introducing the cats. Give the cats treats, or feed them. If the little one is wanting to play. Bring toys out entertain the kitten, and feed the older cat. All depends on the cats priority, some value food more than play, others not.
Have a great time.