It's not a criminal proceeding, the subject has no due process rights, and the check on this power is re-election ever two years.
Pelosi can do whatever she wants, but in turn the President can do as he wishes as well—including ignoring requests for information, and opening Justice Department investigations of criminal conspiracy and treason of the Speaker and other members of the House.
The Supreme Court will have to resolve procedural disputes and the electorate political ones.
The bottom line—The President has everything to gain by attacking the Democratic House even more ferociously than they attack him, using _every_ tool in the tool-kit to make their lives as miserable as possible.
They want war—they get war.
I agree for the most part but The House makes its own rules, not the Speaker, the House. I have seen no vote on how the impeachment is to be conducted or on giving the Speaker plenary power to decide how to conduct it.