This is correct. House can impeach for no reason at all, they only need 51 percent of votes, and impeachment occurs.
Not sure what Q is referring to by asking impeach for what. It doesn't matter.
Obviously if they impeach for a flimsy reason they will look bad in history, but they also won't give a flying fuck about history.
My guess is they would make up something about corruption or dishonesty. Maybe dig out the women who say they were abused. Doesn't matter though.