And as I have said repeatedly, this is a PRIVATE school.
Sorry, but a 17 year old cannot enter into a legally binding "contract" unless they have been certified by a court as being emancipated. (Even then most contracts are void).
No, but her parents could and did enter into a contract with the school.
Any penalty imposed by a governmental agency is a fine. You can't dress it up as some kind of "liquidated damages clause" and avoid the implications of the excessive fines clause.
Once again, there is no governmental agency involved in this case.
On top of everything else, the girl did not even sign the "contract".
I think part of your confusion is sloppy reporting. The "contract" the girl was asked to sign was akin to a "behavior contract" often used to deal with children - an acknowledgement of the rules and the consequences for breaking them. It has no legal standing per se, other than to counter any claim that the student didn't know the rules. Here that is not even a claim - she clearly knew the rules, because she asked for an exception to the rules. The contract at issue here is the contract her parents signed very year when they registered her in this private school. That contract did include the dress code at issue here and also specified the consequences for violation. And as long as her parents signed the contract (which they did or sh could not have attended the school) and were not under duress, then the school has every right to impose the consequences described.
That factoid is not in the article.
If it were a private school, the the student made the mistake of asking permission. She should have put the feather on after she had taken her seat and then asked for forgiveness after the ceremony had ended.
It is always better to ask for forgiveness than permission. If you ask for permission and it is denied, then you can't later ask for forgiveness.
She has some lessons to learn about being a Rebel.