I missed three or more active birth control pills, and this made me get my menstrual cycle again last week, when I just finished my cycle the week before last. I have been bleeding heavily at night and while sleeping. So I waited and restarted a new pack of pills on Sunday. And my period just ended today this Sunday.. do I keep taking the same pack of pills? Or wait a whole week without any pills and then start a new pack next Sunday?

You should have just started taking your old pack, and have missed those few days.
** you know that you will have to go over a month taking them again before they are up to max effectiveness