I don't know. Supposedly you ovulate within 3 days of going off of birth control but of course that makes absolutely no sense since you're protected on the placebo week.

I'd suggest taking a pregnancy test after your next period...
I assume the week has passed, where you didn't take any pills? I would have gone to a pharmacy and asked for pills; many local planned parenthoods will give pills to women at risk.

I doubt that the chances are high for pregnancy.

While it is true you can ovulate after missing 2-3 pills, the odds are not in favor of it, and most likely you will ovulate after missing 14 pills if not more. I didn't get my first period until 35 days off the pill, and I didn't ovulate until day 27 of that cycle (short luteal phase).

While it is true sperm can survive in the woman up to 7 days, most likely it is 5 days and most practically 3 days. This is only given that the woman has sufficient cervical mucus to support sperm survival (this tends to be cervical mucus resembling uncooked eggwhites). Being on the pill tends to dry up cervical discharge, at least it did for me and any discharge I had was white/creamy and not the eggwhite type while on the pill, so I don't think it too likely that the sperm could have survived if you did even ovulate.

The only way to know for sure is to take a pregnancy test if your next period is late. Good luck!