Students at Birdville High have animosity towards their new history teacher. They stage a demonstration outside the school to protest the amount of homework she gives and
each student makes a personal speech expressing his/her feelings about this teacher.
Is this legal under the Bill of Rights?

Yes, the Bill of Rights does protect this.

Explanation:

This is protected under the First Amendment, specifically the "...the right of the people peaceably to assemble...". The First Amendment protects all speech, unless it is threatening violence on another person, as well as any peaceful protests.

There are a few important details that seal the deal when it comes to the Bill of Rights protection. First, they have set up the demonstration outside the school, on public land. If it was on private land, that land owner can lawfully ask them to leave the premises and press charges if they don't. Second, they were peaceful in their actions, making personal speeches about the teacher. The second that protest becomes violent (turning into a riot), they would be removed and their message would lose all of its ground.

So both of these conditions helps the First Amendment create a very strong wall of protection around their case, that is unless the city decides to come and fine them for not having a protesting permit... ;)

Amendment I:

"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances."

four sitting presidents have been assassinated while in office but the first was abraham lincoln,