Would tenured professors who are charged with a crime generally be fired?
Criminal acts are certainly a reason to revoke tenure.  In fact, this is probably one of the most common reasons.  It is possible to terminate the employment of a tenured professor as soon as the university learns that they have been charged with or suspected of a criminal action.  (This happened at my university: it was an extreme case.)  Terminating employment because of a criminal charge is obviously a quite precipitous act to take: I would be surprised if a university did this in any situation except one in which they are sure that the faculty member will/would be found guilty of the charge.  A tenured employee who was fired because of suspicion of criminal acts and was later found innocent of these acts would have, in many cases, a heck of a lawsuit against the university.  (Untenured employees might as well...)

The things that "you heard" sound a little dopey to me, honestly.  Tenure offers some measure of job security.  It does not confer any defense against or immunity from criminal acts.  Getting convicted of domestic violence is "something bad happening to the professor", right?  Not being able to carry out your duties because you are incarcerated is a sufficient reason to fire a tenured faculty member!  In the scenario with the "stalker" it is so unclear what happened or what was reported to whom that I would not be comfortable commenting on it.  Nevertheless, one can certainly imagine circumstances in which a tenured faculty member could be fired for stalking even without a criminal conviction.