A. Yes, she probably could. The legal precedents in cases of this kind have tended to support the right of heads to discipline pupils who have misbehaved outside school hours and away from the premises, provided that at least one of several conditions is satisfied:
* the pupil is identifiable as belonging to the school;
* the misconduct may be damaging to the school's reputation;
* the misconduct is prejudicial to the school's discipline.
Quite often, the issue is not clear-cut and the head must form a judgment on the evidence.
It is, of course, possible that your head accepts that she could have excluded the pupil in this case, but did not do so for other reasons. If the assault was a serious one, it may be that the police are involved and she is happy to leave the matter in their hands.