the catcher was not in possession of the ball when this happened. is the runner allowed to score? is the batter awarded first base? whats the scoring?

As soon as the catcher commits the illegal act of touching the bat, the play is dead and a balk would be called. The runner from third would be given home, and the batter is awarded first base.

It's covered very clearly under MLB Rule 7.07:
"If, with a runner on third base and trying to score by means of a squeeze play or a steal, the catcher or any other fielder steps on, or in front of home base without possession of the ball, or touches the batter or his bat, the pitcher shall be charged with a balk, the batter shall be awarded first base on the interference and the ball is dead."

The balk would still be subject to the provisions of the balk rule, which would allow the offense to take advantage of any further action, such as a hit. Report It

It is called interference on the catcher.

I'm not exactly about the run on third .. I think he would have to go back but the batter would get first base on catchers interference

It's catcher's interference and a balk on the pitcher, but play continues until no further play is possible, then the ball is declared dead.

However, if the batter becomes a runner on the play and he and all other runners advance at least one base, the interference and balk are ignored.

catcher interferrence.
man takes first
man goes back to thrid