It is not illegal. Beyond that, the situation doesn't raise a legal question.

Is this defamation of character?

I am going to assume the accusation was made by the girl your son is alleged to have touched. That is a difficult situation, but it doesn't strike...

Nothing about what you wrote would justify a lawsuit. Since we don't know the specifics of the behavior issues, we don't have a way to second guess...

School requires signed medical exam form for enrollment. Is this legal? Are they allowed to keep entire “long form”??

In general, yes, that is legal. Candidly, it would be more negligent if they didn't have such a form and record.

I agree with Edward, I see zero bases for a lawsuit. Nothing you describe in your answer or subsequent comments raises the specter of...

Probably. However, you should direct your question to a military recruiter.

Maybe. You didn't share the reason the school gave for the dismissal; so for all we know, the dismissal was legitimate. Now, suing may be...

Your story is oddly phrased. You say the math teacher "wrote on her syllabus..." What does that mean? Did he hand write it in just on her syllabus?...

Can I sue a school or a school family for defamation of Character for my son?

Discipline is not defamation. Your son doing dumb things online doesn't make the school deciding to discipline him defamation. If your son didn't...

Not by the new school. As Edward points out, the only real options are to (1) retake the course at the new school to try to replace the grade...