The correct answers are: I am so tired that any coffee will do right now. I have no energy left to study for this exam. I asked my roommates for a caffeine pill, but none of them had one.

Any can be used in affirmative sentences to mean "it doesn't matter which one" (any coffee).

No is correctly used directly before the uncountable noun "energy" (no energy).

None of is correctly used before an object pronoun (none of them).

"Don't have no" is an incorrect double negative; it should be "don't have any" or "have no."

"None students" is incorrect; it should be "No students" (using "no" as a determiner).