What could cause low oxygen levels after a carotid artery surgery and then hematoma removal surgery? Dry esophagus from ventilator?

No. Aspiration or hospital-acquired pneumonia, pulmonary embolism, underlying lung disease would be some of the possibilities.
Low oxygen. Patients having carotid surgery are older. They may have a weaker heart. Extra IV fluid they get during surgery and if they had to go back for a second time to address a hematoma...May have built up on her and can lead to lower oxygen levels. The lungs get a wet and the oxygen can't get through as well. Some time and medications to gradually get that fluid off will help correct the problem.
Lots of things. Low oxygen levels after a surgery can be caused by a large number of problems. Possibilities include ventilator associated pneumonia, pulmonary edema ( fluid in the lungs) adult respiratory distress syndrome, pulmonary embolism ( blood clot in the lung) so without more detail could not say. You should discuss with the doctors involved in the patients care. "dry" esophagus not a cause.