Short answer is no.
The procedure is set in the Constitution. The courts have no say in the matter
Correct. Impeachment is the sole prerogative of Congress and is not subject to judicial review.
Does the President have the power to refer to the AG for an investigation into all the people involved in the plot to remove him by any means?
I haven’t been able to find out if that is crossing the line that he can’t refer an investigation into something that could be criminal in intent.
“The procedure is set in the Constitution. The courts have no say in the matter”
The Constitution is whatever the Supreme Court says it is!
Democrats have been using it against us FOREVER!
Time to turn the tables, at least after Trump’s next confirmation.
Of course he can. It's a matter of finding a court that would give him standing (assuming he is acquitted) and give him the ruling he desires. I think it is doubtful SCOTUS would consider such a case.
The Constitution describes requirements for impeachment with specific words and phrases. Some of those being:
Article II Sec 4. "The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors."
This is easily (and rather obviously) interpreted as saying a President can NOT be impeached and removed just because the House and Senate do not like him. SCOTUS could reinforce that with a ruling that would serve as clear precedent.
Trump may feel that he has a responsibility to protect the office of the President from future frivolous, purely political impeachments.
Of course, there is a down side. What if Robert's SCOTUS takes the case and rules AGAINST Trump, setting a precedent that Congress CAN impeach and remove a President for any reason, even absent of a crime?