As long as the visa is valid and permits multiple entries (not all visas do), I see no problem.
Getting a B-2 visa for a single person tends to be very difficult. If you meet him once, you can get him here on a Fiance (K-1) visa. That is much better if you want to get married.
As far as I know, this should not be a problem if you are truthful about your intentions.
I do not know of any special proof that you can provide. This is purely a matter of consular discretion.
A B-1 visa is appropriate for medical treatment.
If you make the details of the transaction clear to the consulate, I feel you should have a shot.
I cannot give you a hard and fast rule, but generally speaking, CBP wants you to spend more time outside than inside USA each year.
You need to discuss this with your H-1 lawyers. I do not believe you can stay. Filing an extension may not help either.