For the grate in an outdoor grill, I think you can feel safe not cleaning it, but only under the following condition: Before each use, you heat the grill to a temperature in excess of 250 degrees (F) for at least 15 minutes. Gotta heat it up to make sure you kill everything that might have got onto it since you last used it.
Since you really ought to heat the grate up pretty seriously before trying to cook on it anyway, this is almost a no-effort thing.
In terms of extending the life of your grate, it's good to give it a good burn-off AFTER cooking if you're not going to clean it outright. Burning off will make sure there aren't any wet or corrosive things still left on the grate.
As to the broiler pan, I would never let that one go unwashed. Unlike a grill grate, you don't preheat it, so you don't have a chance to kill the beasties that might have grown up in whatever you left on it from last time. If you cooked a steak yesterday and didn't wash the pan, the grease and juices have had 24 hours to attract and breed bacteria and whatever by the time you use it today. Then you pull it out, plop another steak right on your bacteria colony, and broil. What's exposed to the heat directly may get hot enough to kill germs, but what's directly under your steak almost definitely will NOT.
Will you get sick if you don't clean your stuff? Maybe not--it's your life. But please, please, please, don't be so casual about cleaning if you're cooking for ANYBODY else. And really, cleaning a broiler pan isn't that hard. You can man up and just do it.
Simple answer: fewer briquettes. Space them out a bit. You can make fine adjustments by raising the cooking surface or lowering the briquettes. I know my kettle has a lower briquette grill, if you take out the main one. I've also seen briquette grills with sunken channels to create small pockets of heat. I also have a couple of trapezoidal briquette holders, which I can use to position briquettes and create warmer or cooler spots.
Charcoal briquettes are designed to be a consistent temperature. Of course, poorer quality briquettes will be less consistent or burn for less time, but in general any single briquette will burn as long and as hot as any other.
Trying to douse or smother the briquettes may cause smoke or steam, but it's not going to have a good, consistent effect.
Interesting comparison info from Dutch Oven cooking: with a standard 12" Dutch Oven, 12 briquettes in a ring under the oven and 12 spaced around the edge of the lid will give you approximately a 350 degree oven for about an hour. Temperature is adjusted by adding or removing briquettes. This means, in a grill, 24 briquettes could give you a grill temp near 350, if the food is about 2-3 inches away. (The linked chart has a slightly different arrangement; 12/12 is what I learned as a simple rule of thumb, but everyone has different practices... or may desire top browning or bottom boiling.)
Best Answer
Most likely your problem is caused by your dishwasher detergent. Many of them will cause aluminum to oxidize creating the issue you are experiencing.
I would suggest that you hand-wash and remove the oxidation as it looks quite extreme. (You don't want any of it to come off in the dishwasher and be deposited on other dishes.)
While it technically may be 'dishwasher safe', to prevent the oxidation from reoccurring I would recommend going forward that you hand-wash. The other option may be to try different dishwasher detergents to see if you can find one that does not cause this reaction.