The case of interest here would be Tinker Vs. Des Moines. Decided by the Supreme Court in 1969, It held that while the school had a compelling interest in curtailing certain rights that would otherwise be unacceptable violations of certain civil liberties, (in this case the first amendment, though the decision seems to apply to others) speech that was non-disruptive to the school environment could not be denied.
It's a complicated decision, and there has been MUCH discussion on exactly how Tinker does and does not apply, but it would seem to blow several of your arguments out of the water. One, that school districts arn't bound by the Constitution, not being "Federal government agencies". They are (Bound, that is, not federal). They get have special dispensation due to the fact that there is a compelling government interest in educating children, and that interest can justify curtailing certain civil liberties, at least as held by this case. But that shows clearly that school districts are held to constitutional tests, and are clearly NOT outside the jurisdictional bounds of the constitution or the federal court system.
Now, just what contributes to disruptive speech, acceptable curtailing of rights, and other issues has been argued fiercely, often in other SCOTUS cases. However, schools are NOT private entities, and cannot censor at will without substantial cause.