His family doesn't matter as much when it comes to fertility, because you're the one on birth control!
Carifairy actually answered this question really well on another topic. You are protected because that's how the body works is the short answer.
I don't think you need plan b, since the placebo week is almost over. That means your missed period is due to something else anyway, and I really don't think you'd get pregnant right now.
No, missing your period doesn't affect the effectiveness of birth control.