I am 51, and experiencing extreme shoulder pain. Hurts to move my shoulder, can this be arthritis?

Sure. It absolutely can, especially if you have injured it in the past or have an occupation where you use the shoulder a bunch. I would get it checked out by your pcp, sports medicine or orthopedics.
Mosy likely other dx. Impingememt syndrome shoulde bursitis better bets DJD of shoulder is fairlfairly uncommon and comes on slowly stiffness is biggest complaint. Eatry on ac joint arthrist wouldnt be described as severe pain nsaids rest in sling for pain control.
Probably not. Arthritis usually affects the weight bearing joints such as the hip and knee. Shoulder pain is commonly a rotor cuff problem, tendinitis and bursitis known as impingement syndrome.