Can a full spine xray show any nerves being pinched? and a full spine xray include the lumbar region also?

No and yes: Full spine x rays would involve the lumbar area. Plain films can help in diagnosing bone problems, and narrowing of the space between vertebrae, suggesting where a problem with a pinched nerve may arise from, but definitive diagnosis is more specifically acquired by more specialized testing, like MRI and nerve conduction studies.

Yes and no: It will show the lumbar region but an x-ray will in itself not show nerve impingement. You would need an MRI for that.