I have a weird rotator cuff injury. Is it necessary to get surgery?

Not always. The decision to pursue surgical treatment depends on a number of factors, including your age, your activity level, the chronicity of the tear, the size and "repairability" of the tear. Small traumatic tears usually recover predictably well with surgery. Large atraumatic tears often respond to non-operative treatments, although there is some risk of tear progression without surgery.
It depends. See an orthopedic shoulder specialist, who can determine if you'll require surgery for the shoulder.
Maybe. http://www.theshouldercenter.com/arthroscopic-rotator-cuff-repair.htm http://www.Theshouldercenter.Com/video-how-to-choose-a-surgeon-for-your-rotator-cuff-repair.Htm you need a clear understanding of the extent of injury and diagnosis.