Trump and impeachment

I am not familiar with the American legal system beyond the cliches everybody knows. That does not prevent me from wondering whether the sustained, hysterical campaign to get rid of Trump does not have something in common with the legal pretensions on which it was decided not to prosecute Zuma. In short, considering the clear intend to dig for dirt in any way possible, would an impeachment not be polluted by such mala fides (and illegally obtained evidence) that a court might not uphold it? Of course, initially the Houses of the Federal Government would have to vote on the issue. What however would the reaction of the US Appeals Court be if confronted with such result? 

Networks: The White House Leaks We're Receiving Are Aimed at Undermining the President