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).