Is it possible for a woman not to ovulate in a cycle? If so, what's the cause of it

Ovulation. If you get a Period every month then you should be ovulating unless you have Anovulatory cycle which it means you bleed but not having Ovulation, the causes for anovulatory cycle are Hormonal imbalance, Polycystic Ovary, Thyroid dysfunction, excessive weight loss, Excessive exercise, stress, etc. Hope this helps,
Yes. Very complicated "dance" between many, many things for woman to ovulate. Very easy to upset this process. Because many things involved, many things can go wrong to cause a woman not to ovulate. Too lengthy to answer in 400 characters. If you are concerned, please see your gyn provider for question/answer session and eval if needed. Or you can consult with one of the providers here. Good luck.
Possible. It is possible but not probable. At your age, it should not happen. If it does, then you should see a physician to check certain hormone levels.