Its my opponets turns and they have Dazzling aurora and I have one unit at a battlefield, at 7 points. They end turn. Do I score and win or does Aurora abilty go through first then score?

Aurora's ability goes through first, then you score and win on your turn.

Your opponent's Dazzling Aurora triggers at the end of their turn, and the trigger is added to the chain immediately as the turn ends — so it resolves before the turn passes to you (FAQ #4615). Once their turn ends, your Beginning Phase Scoring Step begins: you Hold the battlefield you control, gain the point, and hit 8 — the win happens in the cleanup right after that, not at end of turn (Rules 315.2.b, 472).

Aurora can't stop you, because the unit it plays can only go to your opponent's Base or a battlefield they control — it can't be played to your battlefield (Rule 355.2). This only changes if the unit Aurora pulls has an ability that removes or contests your unit; and it assumes you actually control that battlefield (a unit sitting at an uncontrolled battlefield doesn't Hold anything).