Not talking about the Senate trial (which is presided over by the Chief Justice, btw), but about someone challenging the process on the basis of violation of constitutionally guaranteed rights.
I fail to see how it is permissible for the legislature to exempt itself and its self-made procedures from the requirements of the Constitution.
Because the rules of impeachment are decided by the ruling Party of both the House and the Senate. I believe this is stipulated in the Constitution although I may be wrong.
The legislature was designed to be the supreme branch of government, despite common claims otherwise.
They can cut off money or get rid of anyone in the other two branches.