The constitution appoints the Chief Justice to preside over the trial. Judges have broad discretion. The constitution call for high crimes and misdemeanors. That threshold has not been met. A judge could throw it out.
No. During impeachment the CJSCOTUS is a wallflower. Impeachment is a purely political circus.
The CJSCOTUS’s job is to maintain regular order during the proceedings.
So no Senator is excluded from voting. This is because the CJSCOTUS is presiding.
There is probably some circumstances where the CJSOTUS would intervene or stop the proceedings at his own discretion. Like say every time a pro Trump Senator turned to speak but was shouted down. Or perhaps instead where all pro Trump Senators were shouted down by the liberals.