Good question. If the teacher is at a public school, that information is public record. You should be able to contact the school board or check out their website. They most likely will give you that information in general terms not about a specific teacher. For example in my district the salaries are listed under employee relations. There is a chart that shows the salaries based on years of experience. Another place you can get this information is the local teachers' union.
It is up to each state and/or district as to how much a teacher makes and how much is paid into SS. Some states like mine now take 3% out of our checks to go into our pension fund. Our fund also includes firefighters and police. Each state is different.
If the teacher is a private school, they may or may not be a part of the state pension program.