rules

Yes

Yes, the cue ball must pass the Headstring. If not, than a player could put the cue ball inside of the pocket against the cut rail on the sheft. That would be a heck of a safe.
If the player did not pass the headstring by just touching the cue ball, I would think it would fall under "unsportmenship".

As Straight man said, it has to pass the headstring. But ... if you have no realistic shot even with ball in hand behind the headstring, you do have other options of course to keep the ball behind the headstring although perhaps not frozen to the rail.

You could put it on the headstring and shoot across the short side of the table barely crossing the headstring with enough english to take it back behind the headstring and near the end rail.

You could gently lag the CB down table and back up near the headstring.

Or you could simply pocket the CB in any pocket past the headstring. This option of course gives your opponent BIH behind the headstring. But sometimes giving your opponent enough rope .. like this, could end up hanging him.