Is water, at say 35 degrees F, more dense than water at 80 F?

Yes, water at 35 F is more dense than water at 80 F, so that the hotter water will float on the colder water. But water is special (and almost unique) in that it does expand slightly as it cools to its freezing temperature. Water's density reaches a maximum at 3.98 C (about 39 F) and then actually becomes less dense as you cool it toward 0 C (32 F). That means that 33 F water will float on 39 F water! This bizarre behavior allows ice and very cold water to float above slightly warmer water and keeps ponds from freezing solid. Without it, many animals would perish during the winter.

In fast food restaurants, when they keep your hamburger warm under lights, is that heat from convection or radiation?

Radiation. Convection will take the heat up toward the ceiling rather than down toward the food. But radiation travels in straight lines, from the lamps to the burgers below them.

If lighter colors reflect more light, then why is it easier for a pale person to sunburn than someone with a darker skin tint?

The colors that you see are determined by the visible light absorbed by a surface. Thus, while the whitest skin reflects most visible light and appears white, it does absorb light that you can't see: ultraviolet light. This ultraviolet light is what damages the skin and causes sunburn. Darker skin absorbs most of the ultraviolet before it gets to sensitive skin cells while lighter skin lets that ultraviolet in far enough to cause injury.