What is fainting? Are certain brain cells not getting enough glucose? Is it a problem of not enough oxygen, or something else?

Low blood supply. Fainting is a brief, sudden loss of consciousness due to low blood supply to the brain. The medical term is syncope. The most common cause is slowing of heart rate and lower blood pressure associated with pain, excitement, or emotions - vasovagal syncope. Generally low blood pressure from drugs or dehyrdation are also common. Heart problems are rare causes. Low sugar very uncommon.
Yes. This is a broad question that requires an extensive answer. Fainting can be caused by many things, some fairly benign like low blood sugar, dehydration or over-stimulation of sympathetic nerves (fainting when scared or nervous); and some causes are severe like seizures, strokes (tia or "mini-stroke"), cardiac arrythmias. Basically, it needs to be evaluated by your doctor.