Can spinal cord injury (due to aggressive osteoarth) cause sleep apnea and drops in oxygenation? Still waiting to see if mom's cpap helps w/ o2 stats

Probably not. Sleep apnea can be either mechanical or central. Mechanical is caused by a large tongue obstructing the airways and therefore preventing o2 from entering the lower airways. Central apnea is caused by an injury to patient's brain (not the spinal cord) that causes respiration impairment due to the malfunctioning of the respiratory center in the brain. The spinal cord doesn't seem to play a role.
Possibly. Although the reason is not clear, a 2014 study found that 77% of SCI patients have sleep disorders, mostly sleep apnea. More research is needed. Hope the CA helps your mother.
Pain killers? Spinal cord injury unless occurring at a very high level in the neck, is not going to cause sleep apnea. It might cause hypo ventilation, or not breathing deep enough. Most commonly in these situations, pain killers will cause central sleep apnea by suppressing the breathing center, and also cause shallow breathing with low oxygen levels.