Yes, at 4 years old, he is eligible to enter Pre-K. Application requirements and registration processes for Pre-Ks (public and otherwise) are different for different districts and states. Make sure you check with the particular Pre-K that you're interested in to find out what their requirements are.

Hi, I've linked below a resource you can use to locate schools hosting pre-k programs in your area. The listings include each school's telephone number so you can follow-up directly about enrollment.

Thanks for asking!

Absolutely yes.  I don't think  a child's preschool admission has any thing to do with his /her   the  grandparent's medical situation.

 If you are thinking of what portion of the child care  you may tax deduct or this particular school has any subsidy program that affects such decisions then it is different.  I am not aware of those conditions.  But in general your grand child is very ready to go to a preschool program and they should admit him provided there is an opening.