It depends. Your need for surgery depends on what prompted you to get the study that showed the tear. If you have full range of motion, full strength, good shoulder stability, and can do what you want to do with your arm, then the answer is no. If your shoulder shifts on you, and you cannot do things that you want to do because of it, then you should consider having it fixed.
Depends . Reasons to operate on alabral tear include pain and instability (shoulder going in and out of place). Most people with a labral tear have a normal range of motion.
Tough Question. There are many ways this can be answered. The danger in having silent instability is that the shoulder can slowly progrees towards arthritis and not be symptomatic for years. Make sure and discuss your options with a shoulder specialist that routinely treats lots of these to get the best option for you. http://www.theshouldercenter.com/shoulder-specialist.htm.