relax your risk of getting pregnant while taking birth control is very, very low. Isn't that why you chose this form of birth control anyway?
Taken correctly, the pill is considered 99.9% effective in preventing pregnany.
You would not have your period during pregnancy. Pregnancy is not hormonal birth control. Not the same thing.
Oral contraceptive pills prevent women from ovulating, so no eggs are being made, and with that the sperm cannot fertilize the egg, because there is no egg to fertilize. It also changes the lining of the uterus, thickens the mucus in the cervix.
Talk to your doctor if you are concerned and also make your partner wear a condom.
Relax. You are taking the pill for a reason. Allow it to do it's job.