Answer and Explanation:
a) the advantage if using Nitrogen is that pure nitrogen does not leak out of tires as fast as oxygen do. Molecules of Nitrogen are much larger that those of Oxygen so nitrogen filled tires will remain inflates longer than air filled tires.
b) it is consistent with the ideal gas law (PV= nRT). Volume is inversely proportional to pressure and directly proportional to the temperature which mean that every 10 degree change in temperature will result in 1 psi change in tire-inflation pressure.
c) Yes there is another chemical reason. Air contains moisture which can build up within and corrode the wheels and tire pressure monitoring system resulting in tire rot from within but Nitrogen gas is much drier and allows a more steady pressure inside the tire.
d) No I will not pay extra for nitrogen filled tires because there's no huge difference between nitrogen and air filled tires. Nitrogen contains only about 93-95% nitrogen and the rest air ,while ordinary air-filled tire contains 78% nitrogen and the rest air. Besides nitrogen gas do not protect nor repairs faulty tires, you still have to check your tires from time to time and ordinary air is much cheaper than nitrogen and in some regions free. So I think its just a marketing strategy and do not have much use.