Does "all overturned" mean "Will Hunting denied all the charges (mayhem, theft, resisting)"?

"Overturned" in this case means a conviction for a crime (in this case the crimes of mayhem, theft and resisting arrest) was erased.

So Will Hunting went free without being prisoned?

Yes, at least not for those crimes. Convictions can be overturned for a variety of reasons. He might have presented evidence after the trial showing he was innocent. There might have been procedural problems that allowed him to go free without making a statement of his guilt or innocence. All you can say is that the conviction was voided.

Thank you Engineer.