My mom passed out several times this week. She suddenly couldn't breathe and her lips turned blue. What could be the cause of this?

Go to the Doctor! Your mom could have suffered a heart attack or even a life-threatening heart arrhythmia (not beating right or in sync). Do not delay...Get your mom to the doctor immediately! she needs and EKG and probably to see a cardiologist for a holter monitor at the very least. But in the interim, she is at a high risk of a major heart attack.
Depends. Could be her heart ... Could be simply fainting ... Could be dehydration ... Medications? ... Stroke? ... She should see her md ...