Is there any method or exercises that relieves back soreness, stiffness?

Stretching, yoga. There are many exercises to strengthen the core muscles but yoga (especially gentle stretching) yoga can be great to decrease back tightness. Regular massages, acupuncture, rolfing and feldenkrais are other methods to help with back pain. Try arnica instead of advil (ibuprofen) for pain relief since it does not have all the side effects.
Yes. By strengthening your stomach core muscles or abdominals (abs), you put less pressure on your back. See pain.