First, when your dog shows the first sign of "jealousy" you need to ignore him. If you're standing in a room say "Oops" then walk away from your dog, and maybe lavish your cat with attention. Who cares if he's an older dog, that behavior is not acceptable. If he's on your lap, put him down with an "Oops", and leave him there for a while. If he is calm when the cat comes around, give him a treat, and praise him with a slow and soft "good boy". Always praise his calm good behavior, and completely ignore his unwanted behavior. It is a fairly easy lesson to teach, and I'm certain he'll get the idea. Basically, you want to ignore the behavior you don't want, and reward/ praise the behavior you do. Dogs will pick up on this really quickly. Just because a dog is old doesn't mean that you can't teach it to have proper manners. The dog is new to your home, and you NEED to estabish boundaries for the dog. It will test you, and eventually own you if you don't take charge of that behavior, and kindly teach it the rules of the house.
When we adopted our pit mix, he loved... excuse me... still loves to chase the cat. However, he's learning not to chase her, and to just be gentle if he wants to say hi to her. He really is a good pup, he just doesn't know his own strength. He's come from a horrid background, but even that doesn't matter anymore because he's with us now, and he has to live by our rules, and one of those rules is, no chasing the Mewsaphine...lol.
As for the kennel cough medication, I adopted a pup who was struggling with it, and I never put it in his food. I just gave it to him by hand. If its pill form, just go to Tractor Supply or Pet Smart or any other pet store that sells Pill Pockets. They are tasty little tid bits that you use to hide the pills in. The dog thinks its getting a yummy treat, and takes the meds. I do this with my two large boys who have to take benedryl tabs for their allergies.