If you do the Sunday-start method, it takes seven days for hormonal birth control to work. If you start on the first day of your period, you're covered right from the beginning. If you start at any other time (meaning more than a week after your period stops), you should wait a month.
You're fine.
I agree, eventhough you take it off, it's still in your system and should be effective. How long have you been on the patch? Doctor's usually tell you to wait a couple of months before you have unprotected sex when they start you on the pill since it takes a little while to go through your system, and I bet the patch is the same way. Although, it is possible to get preg. while on birth control, I'd take a hpt. Have you missed your period yet?
Well, since no birth control is totally 100%, I suppose there is a chance. But it's awfully tiny. Hormonal birth control works by suppressing ovulation. If you're not ovulating, you can't get pregnant, and that's why you're protected all month, even on your off/placebo week. It's fine to have otherwise unprotected sex on your off week :-) I suppose you could take a pregnancy test if you're really concerned, but it seems highly unlikely.