Is surgery the only remedy to relieve a cervical spine problem?

Usually last one. Unless you have a tumor, infection, an unstable fracture or one with neurologic issues, a myleopathy, or a progressive neurologic dysfunction caused by spinal stenosis or a disc herniation, surgery should be final option after: activity modification, exercise/physical therapy, time, medication and where indicated: a soft cervical collar, pain management, massage, acupuncture, local heat, traction.
Depends. If the problem is pressure on the spinal cord, surgery may be the best solution. When there is pressure on the nerves, other measures (therapy, exercise, medication) are often effective. If you have neck pain without nerve problems, surgery is usually not helpful.
No. It is actually the last resort. You should first try physical therapy and even pain injections prior to undergoing surgical procedures for correction in most cases.