The cat and the dog are adjusting to each other. They don't fight. They don't get along either. The cat will growl at the dog from a distance. Hiss if the dog gets too close. Its not possible for them to pass by each other in the hall. They sit down and glare at each other.
Aside from that, it's going well. The cat is clean. He knows his litter box. He knows where his food is.
The dog stays out of the cat's food, though she will stare longingly at it from a distance.
I don't know how the cat was treated at RO's. Now he's very sedentary and solitary. They may just be par for the course for a ten your old cat. I bring him out and pet him. He will now come out of hiding when he sees me.
The dog… I don't know what the dog thinks. The dog just wants to play and play and play. Until she collapses from exhaustion. But, the cat, this thing that hisses at her, makes are a little wary. It's really the first time I've seen the dog just sit and stare at something.