I damaged the nerves in my knuckle years ago. Will I inevitably get arthritis?

Not likely. Although nerve damage can lead to arthritis in the lower extremities (charcot joint) it is unusual in the hand. Damage to the cartilage of the joint or a fracture which involves the joint are more likely to cause arthritis than nerve damage.
Not necessarily. Not necessarily. It depends on the mechanism of injury (how you injured your knuckle) and which anatomic structures (ligaments, cartilage, bone) where damaged during the injury. Although intra-articular fractures (bones broken with extension into the cartilage surface) are likely to increase the risk of developing arthritis, injuries to the ligaments (sprains) are less likely to do so.