Can 20 year olds date 16 year olds?

No, its not against the law for a 20 year old to DATE a 16 year old. The definition of date means to go out together to a movie or to dinner or dance. It does not mean having sex

Is it OK for a 15 year old to date a 13 year old?

No. Your grandson and the 13 year old are both too young to give legal consent to ANY sexual activity. This includes fondling with clothes on.