Not with her own egg. Once menopausal, by definition, a woman is no longer fertille, but rather sterile. If a menopausal woman wanted to get pregnant, one option is going through ivf and using an egg from a much younger woman. This would allow her to be a biological mother by carrying the pregnancy, but not the genetic mother (egg from another woman).
Yes. Depends on stage of menapause and if ovulation is still occurring.
Preg post menopause. If a woman has really gone thro' menopause ie. One year with absence of periods it is unlikely that she can become pregnant. Until a woman is really menopausal she may have long cycles, and then resume ovulation and could become pregnant. So if you don't want to become pregnant use contraception at this time of your life!