Why does the grate of my charcoal grill keep rusting?
Rust isn't bad for you, with the possible exception of men who have hemochromatosis. Even then, I don't think that the uptake from iron oxide is very high.

The reason rust forms is due to the high heat the grate is exposed to. Unprotected iron will rust when exposed to the air, and the speed at which it does so is dependent on heat (and moisture). So as the heat increases the rate of oxidation increases significantly. Moisture in the air also causes the iron to rust more quickly, as does the moisture in food as it is cooked.

To remove the rust, use a wire brush before and after each cooking session. Applying a layer of oil to the grate before/after cooking on it will help to keep the rust off. In time, you can (depending on the exact composition of your grill) develop a "seasoning" coating on the metal similar to what you would develop in a cast iron skillet.