I may as well chime in here also, but Chagan has provided most of the same advice.
After grilling, I just close up the grill – that’s after I hit the hot grate a couple of times with a wire brush – and let the charcoals go out. At the next grilling, I just pile some fresh charcoal on top, and dump the lit charcoals from the chimney starter on. Seems to work just fine. I do use lump charcoal.
As for a mop sauce, your imagination is the limit. Just avoid sauces with sugar because that will burn. Here are some ideas: Use about a cup of beer and a cup of chicken stock and add a couple tablespoons of vegetable oil and a couple of tablespoons of red rub. Add a couple of tablespoons of Worcestershire sauce and Tabasco sauce (to taste). Instead of beer and broth, use a cup of cider or white wine vinegar and about a half-cup of water. Warm the sauce in a small saucepan and apply every 30 minutes or so.