Sorry about the giant picture file, but typing up this many questions on Latex would take forever. My attempts are below, I am fairly sure 16+ are right
My answers:
-1T-
-2T-
-3F-
-4F-
-5T-
-6F-
-7F-
-8F-
-9T-
-10T-
-11F - order m-1 right?-
-12F-
-13T-
-14F-
-15T-
-16T-
-17F-
-18F-
-19T-
-20T-\
I'm fairly sure the number you have right is $14$ (maybe $\pm 1$).
Since it's a true/false, I can't in good faith just tell you which ones you got wrong because you're liable to just change the answer. It's nothing personal, it's just a thing. So I will tell you $9$ of the $14$ which you got right, so you only have to review about half of them.
Definitely correct: $$ 1\qquad 2\qquad 8\qquad 9 \qquad 11^*\qquad 13 \qquad 14\qquad 15\qquad 20$$
Possibly incorrect (5+, probably 6) $$ 3-7\qquad 10\qquad 12\qquad 16-19 $$
I marked $11$ because you asked a more specific question about it. You wrote the right answer, but the reason you gave is not correct. I think you were thinking of Fermat's little theorem, but you have to be careful: the ambient group in that context that is $(\Bbb Z/p, *)$, which has only $p-1$ elements; that's why the $p-1$ is showing up there.