Prime is absolutely a life saver, but you still have to do water changes. It does detoxify the ammonia, and nitrites, but it detoxes for only about 24 hours so you still have to get the water changes done.
As mentioned, it won't alter the reading of ammonia in the tank, but it detoxifies it. Both ammonia and nitrites are the toxic byproducts in your tank that you have to remove. When your beneficial bacteria is in adequate quantities those byproducts are consumed by them.
Good tank maintenance helps to keep the bb from being overwhelmed by more decaying food, poo and pee, and gunk than it can handle.
Nitrites are more deadly than ammonia as this interferes with the fish's ability to get oxygen out of the water. Hemoglobin is a component of blood that goes to the gills (same thing in humans, but lungs) to pick up O2. O2 binds with the heme molecule. When Nitrites are in the tank they bind with the heme molecule in the fishes gills and compete with andprevent the uptake of O2. The fish suffocate.
I would get more Prime, use it every water change. On the cory's water change volumn, the best way to know how much to do is test the water. When ammonia and nitrites are at 0 then you're good. If you see a trace of those the Prime will probably cover your butt in regards to his safety, but keep doing daily water changes.
As suggested, I agree that you should keep this up until he looks well and then go a week past that with daily changes. Then just monitor his tank parameters and always keep the parameters pristine.
Prime is advocated by all the expert fishkeepers here, they love it and sing its praises and it has saved my fish on many ocassions, and my sanity.
Your dad's tank probably does have old tank syndrome. The fish have become acclimated to the bad conditions, and too big a change too quickly could kill them.
Gradual changes, as suggested about 25%-30% of the tank volumn would be good and maybe every 3 or 4 days do that.
Gentle, not overzealous vacuuming of the substrate, and keep it too one area of the tank each time... maybe about the area equal to about 20% of the substrate.
Get a baseline reading on the parameters of his tank to see how it stands. Then as you do the water changes test to see that you are getting improvement.
Use Prime in his tank. The bottle says that in emergency situations for nitrites and ammonia levels that are dangerous, you can dose 5 times the normal dose.
If his tank is a 55 then normally a little more than a capful is the normal dose. After the first couple of water changes I would start using the emergency dose (I don't know if detoxified ammonia and nitrite would be a problem with old tank syndrome because the fish are accustomed to higher levels of ammonia and nitrites, so I'd be careful and not use the emergency dose at first), and then for quite a while, until his parameters are good, I'd use the emergency dose. I have done it quite often. I think the consensus is that it would be mighty hard to overdose with Prime.
So the emergency dose for a 55 would be at least 5 capfuls, maybe a little more.
I have overdosed with Prime a lot and my occupants have never had any bad consequences, and I think in this case it would really help your dad's tank.
But, again, I wouldn't do the emergency dose on the first couple of water changes on you dad's tank, but I would on probably the rest of the changes.
When you do water changes, make sure the temperature of the replacement water is the same as the tank. Dose the tank volume not the replacement volumn. So that means even if you only do 30% on the first water change, put a whole capful in the tank because you are dosing for 55 gallons not just the 30%.
Best wishes on your efforts to save your cory and your dad's fish. Keep us posted, we're pulling for you.
