Is a man required to continue to provide medical insurance to his wife after they have been separated for 2 years?

It depends on the divorce agreement. If they have filed for divorce and it is pending, this has probably been addressed in a temporary or interlocutory order. Some states also include a mutual restraining order when the divorce is filed, saying that neither can change the status quo (such as ending med ins) w/o court approval.

If the divorce is final, it should be addressed in the settlement agreement. If it is not addressed, he's probably not under any obligation, unless it is otherwise addressed by that state's law.

If the couple has not filed for divorce, he's probably not under any obligation to continue, but if one of them does later file for divorce, cutting her off without proper notice and making sure she has other options is probably not going to play out well for him in the process of the divorce.

No, because then the man would have married someone else and his name would be put off the check.