Here is a good article which answers your questions in detail. I will post a small portion of what they say:

"But keep in mind that every woman’s body is different and hormone levels vary a great deal from one woman to the other. For a few women the ovaries continue to release eggs despite prolactin production during lactation. So breastfeeding does not always mean that you can’t get pregnant."

The first paragraph in that article tries to answer your question regarding menstruation. It says that the hormone your body produces to stimulate milk production acts to prevent eggs being released from your ovaries.

But, there are exceptions and caveats, so breast feeding alone is not a reliable form of birth control.