Using charcoal in kettle 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.

Well, the answer in each case is really "it depends."

Indirect grilling is a way to reduce the radiant heat from the coals reaching your food, slowing cooking. It's useful for cooking thick, dense foods where the radiant heat might overcook the outside before the inside is cooked through. This isn't desirable for thin foods, where you want to brown the outside of the food while the inside cooks-through.

I'm not sure what the water might be for. I suspect that, because of water's very high specific heat, some folks might believe that it helps evenly heat the air in the grill. Only problem with that is that is your grill has an outlet, either in the form of a vent in the cover or a chimney on larger models. Water vapor is just going to escape. What does stay in the grill is just going to condense on the inner surface of the grill and run down the sides and drop onto your food. Old soot isn't a flavor I want imparted to my ribeye.

Covering the grill keeps hot air near your food, helping to cook the food by convection. Again, this is for helping to cook through foods that might be burned if cooked only by radiant heat.

Indirect cooking is used for longer cooks, like spare ribs or pork shoulder (i.e. true barbecue).

The water pan is used as a heat sink. You can get away without it, although you may find your cooking area is prone to larger temperature swings. Some people (myself include) like to use fire bricks for temperature maintenance.