There is usually still some fat on the brisket flats, but you can leave it on or trim it off if you like. Since you're still new at this, trim off all of the fat from the side with the least fat, and leave the fat cap on the other side to save you some work and headache. That way one side will give you great bark, and the other side some fat. Put the fat side down on your WSM to act as a heat shield. That way if any heat spikes occur, you will burn fat and not meat. Just let the brisket sit there until it's done. No flipping or rotating necessary at all. In fact, brisket is a lot better when you just leave it in the cooker and forget about it until it's done.
I see absolutely no merit in mopping, and gave that up years ago. All it does it waste cooking time with the lid open, and wastes all that stuff you put in the mop. Some people just like to mop though, so don't let me talk you out of it if you are convinced it is necessary.
Good luck, and if you have any more questions, ask away. There's tons of experience on these boards to help you out.