Hi Sandra! First off I would like to say to you and Carl!
Cherry eye is very common in bullies, and it can be removed but it is usually only a cosmetic issue unless it becomes irritated or infected. You can slowly work the nails back with weekly trims, but it will take much time to train the quiks backwards, but with a good clipping schedule they can, believe it or not, go back to where they should be. A dremmel would work best since you can get down to the quik without actually cutting it.
I would just get him current on all vaccines and meds he needs. They will likely want to perform a heartworm test before giving heartworm pills.
Here is some articles on cherry eye and nail trimming, hope they will help!