What Can I Do To Help This Cat?

I hate to say it, but you have your hands full. Sometimes cats that have
problems like this, at this age are almost irreversible. I agree with Mary
regarding putting her in a bathroom until she settles down, and you get on a
normal sleeping schedule, and minimize your damages. Also, granted your
resident cat is neutered and declawed, I would just let them go at it. You
are dealing with two elderly cats, not tigers. They are going to have to
deal with each other eventually, unless you give the newer cat back. What is
the worst that can happen? They scream, hiss and spit at each other? Bonding
will have to be established eventually. I do know what you are going
through. If at all possible, you may want to separate your resident cat in
another room to keep him from screaming at your door, and put the new cat in
your bathroom, so you can get some sleep. That way everyone is a happy
camper for the evening. Good luck with the Feliway. I expect to see updates
as they happen.