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. 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. This is not an unusual situation.