Does a teacher have the right to speak against the superintendent and the school board?

Yes, but in our state it would be job suicide throughout the entire state would do it a different way.

Please see an attorney, and while the answer is generally yes you are putting yourself at risk and should be counseled an circumspect. Free speech has ramifications.

You should first check your union contract or speak with your union President before taking this action.

The teacher likely has that right, but it likely will cost the teacher their job. But I would have to read the contract to give you a reliable answer.

That depends on the circumstances. If the superintendent was observed robbing a bank, of course the teacher may speak to that observation. If the teacher disagrees with the superintendent's lawful exercise of discretionary judgment, the teacher may be at risk for termination upon speaking publicly and disrespectfully as an identified employee of the school or district. Employers even public sector employers are entitled to loyalty from their employees. That is not absolute, of course. But neither is there an absolute right to speak out contrary to the position of the employer.

It depends on school board policy and whether it relates to employment issues or educational issues. Perhaps if they are employment issues, not otherwise. If the teacher believes the school board or the superintendent are doing something illegal, it should be reported to the authorities, not stated in public.