Your pill insert should have information on what to do with missed pills. The one's I've had have usually said that missing one pill is ok (you don't need a backup method). After missing more than one, they usually say to use a backup for 7 days. The idea behind the pill is that you don't ovulate, but that can fail if the pill is taken improperly.
Now, when it comes to inactive pills, you don't have to take them. They are simple placeholders to keep you in the habit of taking a pill daily and to remind you when to start a new pack. You are protected if you take all of your active pills, skip the week of placebos, and then start a new pack a week after the last active pill (so if your last active pill was Sat., start a new pack the next Sun.). It doesn't matter if your period ended earlier than that as long as you took the active pills at the right time.
Sex on your period is no guarantee of not getting pregnant if you aren't protected. Ovulation can be irregular, and sperm live a while in the body, so it's not a safe method. Pulling out is more effective than not pulling out, but it's also not 100% safe. It's best to use condoms anyway, and have the birth control as a backup if you're really not ready to get pregnant. You could also put in a diaphragm if you guys really don't like condoms, as the diaphragm can be inserted some hours beforehand, which means no delay in the moment.
Not just paranoid. You can get pregnant on your period. Everybody is different, it depends on when you ovulate, usually 16 days after your period . When ever you miss one of your pills its not a good sign. Which is why taking the pill is the least effective unless you take it everyday on time. Pulling out doesn't always mean that you wont get pregnant because males pre ejaculate. Even if its a short time frame, missing one pill can cause your medication to not be affective. I don't want to give you information you don't want to hear but id rather just be honest, there is a chance if you missed your pill a couple times and you obviously don't know your ovulation day. What you thought was your period might not have been, sometimes that happens when you miss taking a pill and you release an egg.