How to catch drippings on a charcoal grill

Piling the charcoal on one side gives you more control over your cooking -- because the grill isn't evenly hot, you can move the food around if its cooking too fast. In some cases, you specifically want the lower heat of indirect cooking, such as when dealing with roasts and other large cuts of meat.

The pan of water is often used when dealing with indirect cooking to reduce flare ups -- as the fat renders off, it lands in the water rather than the hot coals starting a grease fire and suddenly heating the item being grilled. As @deroberts points out, it also keeps the air moist, preventing the meat from drying out during the longer cooking period.

You always cover the grill to retain heat for indirect cooking; you're effectively creating an oven, so the item cooks evenly. Not covering the grill will mean your food won't cook evenly, if at al.

For thicker items (more than 2 inch / 5 cm thick), even if using direct cooking, you may wish to close the lid, rather than just cooking from the radiant heat of the coals. You will need to be careful, however, as it means you'll have to watch for smoke, as the fat renders off and falls into the coals. You should be prepared to open the lid to move the food should this happen, or keep a spray bottle of water to take down the flames.

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.