Is it normal for my period not to come while I am breastfeeding?

Yes. Yes, because the hormones from your pituitary gland that help you make milk interfere with the rhythmic timing of the hormones that control your periods. However, do not take this to mean that you cannot get pregnant while you are breast feeding simply because your periods haven't restarted! nature has a weird sense of humor.
Yes. You may still ovulate without menstruating, however, so don't count on breastfeeding as reliable birth control!
Yes. It is normal to not have a period while breastfeeding, but don't count on breastfeeding for pregnancy prevention. It is also normal to resume periods while breastfeeding, and ovulating is possible. If your periods start again it might affect milk volume, but it is still great to continue breastfeeding! whether or not you have periods breast milk is still beneficial for you and baby!
Yes. Though it's not recommended as such, breast-feeding your new baby has contraceptive implications for many women. In other words, breast-feeding your baby can allow you the time you and your body need to replenish itself before it's ready for another opportunity to get pregnant. Again, it is not recommended to use as a form of contraception. Just to be clear....
Yes. Women who are breastfeeding may still be able to get pregnant. If a new mom gets pregnant with her first ovulation a few months after delivery, she will not even have a period until after the second baby is born. A urine pregnancy test can tell whether a breastfeeding woman is pregnant or not.
Yes. Women generally experience return of their menstrual periods when the baby begins solids and breastfeeding decreases in frequency to every 4-6 hours. Remember that this means return ovulation so make sure you are using contraception.