Yes. Nerve root impingement is the major cause. Piriformis syndrome can do this as well. If this continues, see a rheumatologist or orthopedist. I would get emgs done by a neurologist or physical medicine specialist, if you truly have radicular pain.
Yes. Significant spine arthritis can be accompanied by either foraminal stenosis (narrowing) or central stenosis (narrowing) which cause pressure on individual nerves or groups of nerves which would account for your symptoms. The diagnosis is usually made with physical exam with our without MRI of the spine.
Spinal stenosis. The arthritis in the spine could be compressing the exiting nerve roots from the spinal cord causing numbness down the legs. If the back pain and symptoms down the leg (s) become too debilitating then surgery would be recommended. A spine surgeon consult would be advised. Obviously if bowel/bladder issues start then this surgery becomes urgent. Good luck.