My question is how safe would it be for a lone backpacker in the NF?
Due to my bad back I don't want to backpack with a group, cause I may not be able to keep pace. Alone, I figure I could go at my own pace
That really depends on the individual and the environment. It certainly is more risky than camping with a partner. The biggest risk (aside from a terminal injury) is an immobilizing injury and in an unknown, rugged terrain obviously the odds of this happening are greater than, say, during a walk to the park. Also, if you break your leg in a city park, there will likely be plenty of people around to help and your cell phone will probably still work. If you are off-trail in a NF you might not see anyone for days or weeks and cell coverage is usually poor.
I would definitely recommend starting slow, like you have been doing, and build up to longer hikes. Leave someone a detailed itinerary of where you are going and when you are returning -- and have them check to make sure you made it back. Bring a whistle and learn the signals. Ask yourself, "If I am stuck on the forest floor for 4 days with a broken ankle will I have enough food and water to survive? Will I be able to keep dry and warm at night?" You have to do your best to prepare for those situations and understand that there is still risk since it is impossible to prepare for all possible outcomes.
Then you have to balance that with your mobility. You can pack in all kinds of things for those "what if" moments but that all adds weight which not only makes the trip less enjoyable but also increases the chance you will injure yourself.
I'm leaning toward a NF cause of the disperse camping policy:
Dispersed camping is allowed anywhere in the National Forests as long as you are:
1000 feet from roads open to vehicles and parking/recreation areas
Not in a managed wildlife meadow
Not in a specially managed area such as Bent Creek
Which brings me to another question... Another site defines dispersed camping
as primitive campsites in designated camping areas. Any one knows which (dispersed camping definition for North Carolina) is correct?
When in doubt call the ranger's office for the park in question, but in a NF the "designated camping areas" for dispersed camping are the areas not explicitly reserved for other uses (which would include actual designated campsites, preserves, etc.). They make it sound like there are small, scattered areas reserved for designated camping when they really mean the vast majority of the forest. The wording on the forest service web site is definitely confusing.
Generally they prefer you camp somewhere that is not visible from the trail(s) -- though that is not always possible. Try to camp at least 100 feet off of a trail. Don't camp directly in/on scenic points of interest. Sometimes the forest service just bans camping in certain areas that are popular with tourists. When people take a picture of a waterfall they don't want your tent in the shot.
You will need to have a trowel that you will use to dig a 6+ inch hole with to bury your human waste (not garbage -- pack that out). Keep that well away from trails and water sources. Again, dealing with human waste varies from forest to forest. Some places require you to pack out everything -- yes, everything. Again, talk to a forest ranger for park specific rules.
Then there is water purification, hanging your food, don't eat where you sleep (in bear country anyway), camp fires -- are they allowed? (Ask the ranger) I'm sure you've already had to deal with some, if not all of this so I won't go into more detail.
I've never been to the Smoky Mountains, it looks like a beautiful place. Good luck!