For shops- in Brianhead, Georg's is a great shop with a knowledgable staff. In Cedar City, (just down the mountain) I'd highly recommend Brian over at Cedar Cycle. He is a great guy and willing to help out with anything.
Camping options are open, if you want to camp in a designated campground, you can go to Duck Creek, however over the Holiday it is 100% packed with Vegas folks and their campers, kids, and everything else. Actually, a lot of the designated campgrounds up on the mountain will be full, Cedar Mountain is like the designated Labor Day vacation spot for the state of Nevada. There is camping at Cedar Breaks, but I've never looked at their facilities. An option might be, depending on if you get up here before Friday, is a brand new campground up Parowan Canyon at Yankee Meadows. Most campgrounds up here don't offer showers, only water faucets every few campsites, and some bathrooms (open pit or regular).
In case you don't know, there are 2 main ways up to Brianhead. You can travel up Hwy 14 from Cedar City to the Cedar Breaks turnoff, and up and over to Brianhead. Or, go 20 minutes north of Cedar City to Parowan, and head up Parowan Canyon. Up Parowan canyon there are 2 main turnoffs - 1st left and 2nd left. They actually connect at the Yankee Meadows resovoir so it is basically a loop. However, if you turn up 1st left, there are 2 campgrounds. One is only a mile or so up, BUT I don't know if it is open yet. The other is about 3-5 miles up, and is a much better location. Both are accessible with cars. The second campground is only like 1/2 - 1 mile after the pavement ends.
Overall, best bet for camping up on the mountain is to get here before Friday, and you should be able to find a spot.