So part a) is fine.

part b) I can show it's not an ismometry (with values x=4, y=1 as a counterexample). But showing it's a homeomorphism i'm a little confused, as it's the identity map, will I simply have to show that y=x is bijective, continuous, and it's inverse is continuous?

part c) I'm not really sure on how it affects this.

help would be appreciated, thanks.