Could be, yes. Your symptoms are quite vague. Many things can cause lower facial pain, including impacted wisdom teeth or other dental problems. But, if the pain is worse when you're moving your jaw or chewing, it's likely to be a TMJ problem. Often these pains are referred to the ear, just in back of the jaw joint. A panoramic x-ray to rule out other problems may be indicated.
Pain. You should see a dentist for a proper diagnosis. The pain could be from a tooth or gum infection. Possibly tmj, but usually the pain is more in front of the ear area. A dental x-ray may be needed.
Depends. Need to be evaluated to make sure that you truly have tmj/tmd or some other ailment, etc. That can mimic TMJ symptoms. Should see a dentist/tmj specialist first to give you more info with a thorough history and exam.
Could be. Yes, it could be TMJ but there are many possible explanations. Ranging from a dental problem, to something much more serious. Start with a dental or oral surgery evaluation.
Yes. Your muscles may hurt because of tmj.