Is a laminectomy or vertebrae fusion or both any good to relieve back pain?

Depends on the pain. Back pain can be caused by many sources: muscles, nerves, discs, joints etc. In the back. If your particular pain is caused by nerve compression as might be seen on an mri, a laminectomy procedure to remove the pressure can greatly relive pain. An epidural injection often helps predict how well a laminectomy might work. Fusion is preferred when there is instability or seve joint or disc problems.
Both. Both operation can performed successfully and have good outcomes when the surgery is performed for the correct reason. There is no one surgery fit all procedure. The proper diagnosis must be established so that the proper procedure can be determined for each individual. Talk to your spinal surgeon.
When needed. The surgery has to match the correct diagnosis to have a chance of success. Also, factors that can negatively hamper a correct surgery include smoking. Even with all things done right, there can be less than full satisfaction with surgical outcome.