Can I call sperm bank to get update on health history of donor and his family since I had his child?

Yes. It is usual to get a medical history of donor before insemination. Unlikely that a donor will inform sperm bank of any changes in his health after donation, but, no harm in calling to find out. Good luck.
Yes. If you received sperm from a certain donor and had a term pregnancy, they will likely give you any updated information regarding that donor since any material fact and information will directly affect you and your baby.