All very good questions. Exercises using the Swiss ball have become very popular. Using the ball may help strengthen the core muscles. The core muscles hold the bones in the spine together. They are deep inside the trunk and give us stability rather than generating movement.
Core training is used by many people to prevent back injury. Athletes hope to improve performance by doing these same exercises. Patients with low back pain include them in their rehab program. The truth is there's little proof that one type of exercise is better than another for acute or chronic low back pain.
Most studies support the benefits of a general exercise program. Unless you're training for a specific sporting event, it's best to engage in some kind of exercise on a regular basis. Find a form of exercise you like and vary your program. Your body and your health will both benefit.