How is Zenkichi able to see now that he has lost Parasite Seeing?
I believe it has something to do with how Model Zenkichi works. This lets him see his own limits, so it lets him see what he is capable of. Thus Fridge Logic tells us that if he can see what he can do, in order to succeed all he needs to do is act on that. For example if someone throws a punch he is theoretically capable of blocking it, even if he can't see it. Thus he won't actually see them throw it in the way you and I do, he will see whether or not he is capable of blocking it, and if he can how he would do it. Then he does that, and blocks it. Or hell, maybe Model Zenkichi or Anshin'in just fixed his vision for him. Occam's Razor would dictate the latter.
I believe its more of the fact he was given eyes that had Parasite Seeing, that he still retains the eyes to see normally but isn't able to see other people's view now.