Acts of Antisemitism can be the basis of a legal violation, so long as those acts create an interference with the ability to do one's job or to participate in one's educational experience.

K-12 public school teachers do NOT have free speech rights in the classroom or whenever they are performing their official duties. Private school teachers have greater leeway, as do college professors.

It depends. The U.S. government has slowly begun to recognize that anti-Zionism can constitute antisemitism, and so is subject to anti-discrimination laws, when such hostility goes beyond merely criticizing the Israeli government for various policies but instead attacks Zionists or Israelis for things the speaker doesn't criticize other countries for doing. This is why it is so important for institutions and governments to adopt the IHRA working definition of antisemitism and its examples.