I agree.. if he is still eating and is not in pain, then there is no reason to put him to sleep. Fleas should not be a problem if he is given the correct flea treatment.
If you don't feel you can give him the care he needs, then I would look for a senior rescue near you to take him.
I hope all works out for you both, it sounds like he doesn't have much time left here on earth, maybe you could just make the rest of his life good for him!
I understand you didn't know what you were getting into when you took him in, and that is NOT your fault.

The person that gave him to you should be ashamed of themselves!!!