Normally, no. Consult Urology. There are medications and exercises. The are bladder rehab centers.

This is a complex question which requires a lot of background information. You could have overflow incontinece, meaning you have a very difficult time emptying your bladder, it becomes over filled and spills over.
You could have a neurogenic bladder with a small bladder with sever contractions that causses leakage. you could have a bladder stone that is acting as an irritant. Without knowing a detailed history, there is no yer or no answer to your question

Yes. And cystogram

History and physical exam is needed. Is it post-void dribbling? Is it associated with coughing or sudden strain? A urologist can work up the condition and run a few tests to determine what kind of leakage and how can be treated.

Bladder leakage surgery is a surgery done to improve the quality of life of the patient. If you have any reservations about the surgery seek a second opinion.