What is the punishment for both the Professor and the student if...?

As far as I'm aware, consensual relationships between professors and students are not illegal or against any rules per se. If this led to manipulation of their grades or something like that, then it could lead to disciplinary proceedings, but the relationship itself is not something you could get into trouble for. If there was any element of sexual harassment, of course, that's another story. Unless the student was using it to get extra grades, no penalties for them either.

Likewise, if they got married, no penalties I can think of. Also, serious relationships like this tend to be treated more leniently, ironically. People sometimes look down on illicit relationships, but marriage usually gets celebrated.

depends on both school rules and state laws
many don't allow teacher student relationships - because the teacher can affect grades and it is also seen as taking advantage of the student at any age or the student bribing the teacher
the teacher could fired and even jailed
the student could be expelled

Professor still gets fired.