Is it likely to get some stress injuries to incisors, molars, or your TMJ if you snack on turkey jerky 2-3 times a day, to avoid sugary snacks?

Not likely. Not likely, unless it is very hard jerky. You'll start getting some symptoms before damage.
Jerky Teeth Injuries. Thankfully, no! i enjoyed some beef jerky last night that my son brought from england which was produced in south africa..The best I have ever tasted. Strong teeth and gums will not be damaged by almost any food you can digest.
Very small risk. Anything is possible, but the exercise is probably better for you than sugary stuff would be.
Sure. It is important to vary your diet. Jerky is very tough to chew and could put excess stress on the jaw joint, particularly if eaten often. It's probably too much sodium, also.