What is your definition of measurable? I assume you mean that
for each Borel set.
So here are some hints;
First show 2) by considering sets of the form [a,\infty) then show 1 by using the 2 complement and sets
For 3 consider sets of the form .
Q2 is wrong, you need the function to be surjective. You should attempt it first (and post here).