I had heard there was a new law regarding work duties that are taken home after work hours. Specifically, study materials for work related schooling. I was told this was no longer allowed, that any necessary studying must be done while on company time.
Is this just for work related instruction? Does it apply to any job?
Does it affect teachers who spend hours at home grading papers?

There is no such "new law". You can bet it would have been publicized like crazy. Studying for job-related classes on the employee's own time is not normally compensable.

And most teachers are exempt, anyway, so they aren't going to get any more compensation for doing work at home.