can a mat judge (the second official) come and try to convince the ref who had already awarded points (for a takedown), from reversing his call without being asked by the head ref for his opinion?

The assistant referee can bring anything to the attention of the referee.

The lead referee can agree or disagree with the assistant (NFHS Rule 3.1-3.2) and his decision is final.

Can and should. If the assistant saw something that the official did not, for example, an out of bounds situation, then he has every right and the obligation to speak up. Whether he will is a different matter.