Can you miss your period while on birth control?

Yes, it's possible. What exactly are you asking? Some hormonal contraceptives can eliminate a woman's period altogether. Others, such as many forms of the pill, allow a woman to control the timing of her period, even use them to skip over her period by skipping the inactive pills (and going straight to the new pack with no delay).

If you take the pill every day, or take whatever form of hormonal contraceptive you are talking about faithfully as instructed, it is highly unlikely to get pregnant; skipping periods can be alarming, but is generally not a problem. Consult a doctor if you're worried, but it's really not likely.

depends on the birth control. Some make it so you force your period every month by taking two sugar pills. Others make it so you have a period every three months.