> The Constitution requires a high crime or misdemeanor. <
Yes. But the Constitution gives the House the sole power to define just what those terms mean. As an example, Benjamin Franklin once remarked that a President could legally be impeached just for being rude!
IMO impeaching Johnson for violating the Tenure of Office Act was simply a construct for impeaching him and the real reason is that he wasn't being "tough" enough on the South. That SCOTUS later deemed the Tenure of Office Act unconstitutional shows it for the purpose it was enacted.
No it doesn't. It gives that power to the Senate who have the sole power of trial.