Incorrect. Generally a glenohumeral dislocation would require a grip/pull on the arm in a inferior direction, while in this case the obstetrician gripped the head.  The shoulder at the clavicle/acromion would have been stuck, not the arm.

Incorrect. Fracturing the humerus during delivery would require gripping the infant limb and applying considerable force to fracture the bone. In this case, the obstetrician gripped the infants head, not their arm.    

Correct! This is the classic mechanism of injury for a birth palsy, where torsion on the head/neck with a stuck shoulder produces a stretch injury of the brachial plexus.

Correct! The presence of a congenital malformation, such as a supernumerary (extra) cervical rib could be causing compression on the brachial plexus. The syndrome can be present at birth, though it is more common to emerge later in childhood after the bones have grown in size. 

Incorrect. While this is a brachial plexus palsy that can occur at birth, the mechanism of injury is generally from pulling on an arm extended above the head. This could occur in an infant if the obstetrician pulls the infant out by an arm if the arm emerged first, but in this case the head emerged normally and was grasped.

Incorrect. Although, while rare, an infant radiculopathy can occur the arm is innervated by cervical levels so a mid to upper thoracic nerve root compression would spare the upper limb.

Incorrect.  The infant could have experienced a trapezius strain during birth due to the stretching and pulling of the neck and shoulder during the delivery. While the pain might result in limited motion being made by the infant of the shoulder, there should be normal wrist motion as that is unaffected by trapezius and the scenario described a limp wrist.