Is your cat peeing somewhere? If they don’t pee in 24 hours, thats a vet visit. Just had to take mine in to the ERvet for that. Make sure she is drinking plenty of water. 13 is only middle age if she’s getting regular checkups and love :)
I wouldn’t worry about the kitten too much, they’ll come around. I think you’re doing everything right so far! As the other commenter said, introducing them through playtime could help, or doing the trick of feeding them near each other. (Which is easier if your cat is food motivated, but it doesn’t sound like old lady is, ahh the struggles)
Nah they’re just an active user with good memes