How do we know that he doesn't accept that YOU are old? Would we need to write "que você está velho."?
Yes, it makes sense. We use pronoun to avoid confusion!! (as in this case). When you do not use, it means it is the same.
Not exactly. The context makes it clear that the person became old and now, at this point of his/her life, the person is old.
How about "He doesn't accept what is old" in a context as "he doesn't accept anything that is old"
In your translation of velho , you give the possebility to choose for "old man"