Michael, Let me see if I can help a bit. I would suggest the GSMNP as a trip location for you. First let me recommend a few resources. The first is the National Geographic Map of the park, map # 229. The next is the "little brown book" entitled Hiking Trails of the Smokies by the Great Smoky Mountains Association. It contains a small easy to carry map of the entire park and has detailed trail descriptions of each trail and camping location. The last is Trekking the Southern Appalachians by Backpacker. Trek #12 is a 53.8 mile loop as one possibbility, but you can easily build other loops. You might want to include a loop that hits Clingman's Dome (highest point in the park along AT). A loop like this would be something like Lakeshore Trail to AT to Clingman's dome to Forney Creek trail south back to Lakeshore trail (not sure miles, but its fairly long 50-70 miles?).
Now for logistics. There is no fee for backcountry camping in the park, but you are required to camp only at designated sites. These sites are typically flat area with water access and food/bear hanging cables. There are a few sites that require advanced reservations, these are shown on the National Geographic map. Beyond those sites you can camp at any site you like. I wouldn't worry too much about max number of people, you should be able to share a site with any group. You are required to register at a Ranger station, but you can do so even if it is not open. There is a drop box for you to fill out your itinerary. There is a ranger station right after you enter the park on 441 near Cherokee.
As far as toilet...pee freely just not near streams. Poop...find your own spot away from a stream. Dig a small hole six inches deep, poo p, and bury.
Hope this helps, I'd be glad to answer any questions I can. I know figuring out hiking logistics for a new place is always a pain.