if i just won my 3 game series to advance and have 0 points in my new division, does that mean if i lose my next game i am demoted back to the previous?
It might be 3 loses in a row to fall, but I don't think that's it. I think it's connected with the same system that decides how much LP you lose/gain per match. Just like you lose a ton and gain very little if that system believes you are in too high of a division/league it would drop you if you are too high or keep you at 0 LP if you are fine.