What might be the cure of my recurring shoulder pain?

Various. Sounds like a chronic recurrent soft tissue injury like a tendinitis. It might be related to. Certain activity or repetative motion. Tendinitis usually hurts when you push on it. A single injection of cortisone might be curative.
It depends. Could be a tendinitis, or something more serious like arthritis or a rotator cuff tear. See an orthopedic shoulder surgeon.
Many reasons. At your age, the most common cause of true shoulder pain is a rotator cuff issue. Either tendinitis or a small tear. It can also be a biceps tendon issue or even arthritis. Shoulder pain could also be referred from neck issues such as a pinched nerve. If it is chronic in nature, i would get it looked at.