Usage of “per”, “each” and "every"?

Can you tell me which ones are grammatically correct and why?

Students must study for 20 hours per week.
Students must study for 20 hours each week.
Students must study for 20 hours every week.

Students must study 20 hours per week.
Students must study 20 hours each week.
Students must study 20 hours every week.

I am also not sure is it necessary to have "for" after study.

Please help thank you.

If you "study 20 hours" this is ambiguous: It may mean that you study an important period of history which lasted 20 hours. An example might be the moon landing or the use of the atomic bomb.

So to be clear that the period of 20 hours is the time devoted to study, rather than the time studied, the word "for" is required.

Other than that, the difference is not in the denotation, the primary meaning, but in the connotation, the additional meanings which are carried with it.

• "per" generally means an averaging. One may study for 5 hours one week, and 15 the next, and achieve 10 hours per week.
• "each" generally means either an equal distribution, or a minimum, or both. Studying 10 hours each week would mean at least 10 hours every week.
• "every" in this case means the same as "each" but with more emphasis on the consistency, that there can be no missed weeks.

So in this case these words are almost the same. It is only the additional feeling, or connotation, which is different.