Impeachment. like most criminal cases works a little like chess. The king is never actually captured. The loser resigns when capture is obviously unavoidable. Most criminal cases end when the defendant cops a plea.
Inability to do the job doesn’t require a criminal standard of proof. Leaders of governments get dismissed in many a democracy for all sorts of perceptions of unsuitability, not necessarily wrongdoing or precisely-calibrated incapacity. “I’ll lose my seat if we don’t get rid of [him/her]” will often do it.
The US constitution sets fixed terms. Impeachment was intended as the mechanism for removing someone before their term is complete. It requires proof of a crime. In the cases of Johnson and Clinton, politicians in congress twisted themselves into knots creating a crime with which to accuse the president.
Democracies that have been established more recently provide easier ways to remove the head of state.
Yes and no. “High crimes and misdemeanors” does not necessarily mean only an actual, indictable crime – other forms of misconduct and abuse of power, which are not actually criminal offenses, can also be grounds for impeachment. Fundamentally, what is impeachable comes down to what Congress chooses it to be: