So my friend just got the results back of his paternity test with some one night stand he had, and it said there is a "0% chance" that hes the father. since it wasn't done through the hospital, i guess its not a legal one, and he has to get another one done through the hospital to get his name off the birth certificate. but my question is, is it possible that the hospitals test can come back that he is the dad? even after one already said he isnt?
i would understand the hospital saying hes the dad if there was like a 5% chance, or something like that, but a "0% chance"? that seems pretty hard to screw up and not get ANYTHING to match up.
he has all intention of doing a legal test now, its just going to be more difficult because now hes overseas. he was able to take the original test while he was home on leave. i was just wondering if it would be possible for the results to come back positive even after the at home test.

Your friend needs a legal test now or face the possibility of paying for a child that is not his for 18 years. Legal test = 'chain of custody' + accredited lab + samples from all parties.

The home test could be wrong.

Does our legal system require DNA paternity tests when child support obligations are disputed? Does our legal system require DNA paternity tests when child support obligations are disputed?

Doesn't require DNA test but you may request testing through the courts.

How do you legally subpoena a third party if you think he is the father of a child especially if he refuses to submit to DNA testing? How do you legally subpoena a third party if you think he is the father of a child especially if he refuses to submit to DNA testing?

You don't.
You file a request with the court, who then decides if they will ORDER the test. Subpoena is just an order to come to court. When there is an order, it is not his right to refuse, unless he chooses to be cited for contempt of court.