I just learned all my definitions. I know understand everything thank you for the advice it really helped a lot
Yes, you can. HallsofIvy just proved that f is surjective, but first he said what it means by definition.
Yes, you do.
I would recommend reviewing or asking your instructor to explain how to prove statements of the form "For all x, P(x)" and "There exists an x such that P(x)." But above everything else, make sure that you know definitions by heart!