Tell me if dental problems cause headaches, neck pain and pain in the lower back?

Yes, yes and no: It could possibly cause headache and neck pain but not low back pain.

It's extremely rare: Irregularities in the positions and the alignment of the teeth can and do cause a host of problems, among which headaches are not uncommon. Certainly spasm in the muscle of mastication can cause neck pain. Lumbago is among the uncommon sequelae, and frequently has other etiology, but just to make the point, chronic neck spasm can cause a curving of the back with raising of the hip and sciatica.