Yes, a girl can get pregnant even if she never had her periods. Getting pregnant has more to do with ovulation. Some women ovulate and release eggs from their ovaries before getting their periods started. Hormonal imbalance can also be a reason that a girl doesn't get her periods but it doesn't mean that she cannot get pregnant after having sexual intercourse.
Yes. Ovulation timing is important for a woman to get pregnant. So, if periods are irregular or even do not occur, then pregnancy can occur successfully. If you have any doubts, then you need to consult a good gynecologist for the results.