No
Cotton absorbs water (sweat) better than polyester, therefore causing an odor (smell of sweat) to be given off when worn (if you sweat, that is).
Depends on intended usage and preferences. polyester dries faster but is less resistant to heat.
Cotton is much warmer that polyester.
Polyester is a category of polymers which contain the ester functional group in their main chain. However! the term "polyester" as a specific material most commonly refers to polyethylene...