Let the older dog set the pace. Many dogs love playing with other dogs. I have a golden that's seven years older than my collie puppy and she has waayyy more energy than he does. When the older dog is done playing, give them a space where playtime is over and they don't have to worry about the younger dog jumping them. After that, it's time for someone else to step in to play with the puppy until both are tired.

A tired dog is a good dog. Up the exercise your dog gets in a day and make sure they have plenty of toys they can chew. Also check out how your dog is feeling. Chewing can be a sign of anxiety or nervousness in a dog.

Your puppy could be very excited! Dogs with a lot of energy need more exercise, or else they'll find they're own solution. My puppy gets the zoomies and will run laps in the house like crazy when it's time for food, they think someone's coming over, or they're just bored!

My dogs are greatly concerned with cats. Just be consistent with your training. You could also do association work with your dog if you're still worried. In a training session, every time the dog can ignore/leave it/gentle touch the cat equals a click and treat.