1. Are there backcountry sites where I can have a fire going or is it all off limits?
All backcountry sites has a fire ring with the exception of the Mt. LeConte backcountry shelter. There are no fire ban in the Smokies, but maintaining a fire can be challenging due to constant wet conditions of woods.
2. What would be a decently long and light-moderately difficult trail?
Define decently long and light-moderately in terms of miles and elevation gain. Everyone has different definition of this. lol.
3. Any reccomended backcountry camping sites?
37 at Walnut Bottom on Big Creek is a huge campsite and it's a easy hike (6 miles from the Ranger Station's parking lot with 400-600 feet of elevation gain) 69 is a quality campsite on a river. The campsites all along the Little River Trail are nice too. Keep in mind, some campsite requires a reservation. Walnut Bottom is one of them. As well as Mt. Sterling and few others. There is a list of campsites on the park's website on which one requires reservation and which one that don't. The ones with reservation requires you call Backcountry Office and inform them, then they will give you a reservation number to write on your permit on the day of the hike. If you choose to camp at a site that don't require a reservation, you simply show up and fill out a permit without making any calls to the Backountry Office.
4. How much water should I bring for two people for two days?
Depends on the route, a lot of campsites are near the creeks. There is A LOT of creeks in the Smokies. Many shelters have springs where you can get water. If you can, get a National Geographic Map of the Smokies and they've done a good job of being accurate of where the springs are located along the trails. Least only to the extent of where I been and saw the springs personally.
In another words, to my knowledge they exists, but cannot tell you if they're dried up or no longer exist.
Let me know if I can be of further assistance. I live about 30 miles or less from the nearest ranger station in the GSMNP. I'm about 1.5 hours depending on how bad the tourists are clogging up traffic from the park's headquarter.