How long it takes you to get pregnant depends on your body.
Some people can be on the pill for twelve years, quit taking it and be pregnant within a month. When someone else has only been on it for one year and it takes them a year or more to get pregnant.
It just depends on your body. Just relax and have fun doing it. If you stress yourself out, it will be harder to get pregnant.
As for your period, you can have implantation bleeding if you are pregnant, and some women do continue to get their periods during pregnancy.