Trump is not on trial the way we usually think of a criminal trial.
It's not, strictly speaking, a legal event at all, and not even a part of the criminal justice system.
Despite his previous public statements, he has no right to due process, because he's technically not accused of being a criminal.
He's accused of violating the Constitution.

Impeachment is not a prosecution, despite the Republican Senators using language that implies as much. Calling for the House to send the Articles of Impeachment in a "timely manner" reflects an accused criminal's right to face their accusations in a timely manner.
It's a smoke screen to confuse the court of public opinion.

There is no appellate process following impeachment. Whatever ruling the Senate makes is final.
Impeachment is a legislative branch process.
The Supreme Court has no jurisdiction over impeachment matters, despite the Chief Justice ruling over the Senate impeachment proceedings. Note, the Chief Justice has only an advisory role in this matter. The Chief Justice has no authority in impeachment.