Doctors, can my current back problems cause pain and problems with my neck?

Generally No. Back Problems cause back and leg pain. Neck problems are due to the neck. So each area generally addresses the nerves closest to it. We do know that those patients with spine problems in one area of the spine, usually have a higher risk of developing spine problems in another area of the spine.
Depends... trapezius strain can cause neck and back issues since it attaches from base of neck and spans to mid back.