Winning the game on Minefield with no cards in decks. If we are both at 7 points, I have no cards in deck and conquer for the win on Minefield, what happens? Do I win before Minefield triggers and gives 8th point to opponent?

Let me clarify the scenario you're describing. I'll assume you mean you're at 7, held or conquered the other battlefield earlier this turn (otherwise you can't "conquer for the win" at all).

Yes — you win before Minefield's trigger matters.

Here's the sequence under Rule 466:

1. 466.1 processes first when you Score. Since you're at 7 and you've Scored every battlefield this turn (one via Hold or prior Conquer, this one via Conquer), you Gain the Winning Point under 466.1.b.2 — you go to 8 and win the game immediately.

2. 466.2 then says "Trigger Score abilities at the Battlefield that Scored" — this would put Minefield's "put top 2 cards of your deck into trash" trigger on the chain. But the game is already over from step 1.

The win from gaining the Winning Point ends the game before any triggered ability from the battlefield (including Minefield's mill effect) ever resolves. The empty deck and the potential Burn Out giving your opponent a point never become relevant.

If you haven't scored both battlefields this turn, though, the opposite happens — per 466.1.b.2 you draw a card instead of gaining the point (staying at 7). Then Minefield's trigger resolves, tries to mill 2 from an empty deck, causes a Burn Out (Rule 431.1.b), and your opponent gets the 8th point and wins. So the answer depends entirely on whether this is your second scored battlefield this turn.