1- Clay bar is just a small block of clay. Very effective at removing above surface contaminates such as tree sap, paint overspray, etc... Very easy to do, but you must rewax your car afterwards.
2- There are all kinds of products out there for rubber. Just pick something that contains a rubber conditioner and UV protectant. Any auto parts store carries these products.
3- Not sure about how tough it would be to get a dealer to respray your hood. But are you sure it's paint failure? Could it be oxidationor something like overspray on your hood? Pictures would help here if you can get them. It may be easily removed without repainting your hood, or it could be paint failure.
4- If your talking about the outside surface of your headlights, you could put a coat of wax on them,or use a dedicated plastic cleaner wax.