[color=darkblue]1. Stunts - the rules say stunts should rarely impose more than a -2 AV penalty. They don't have a Difficulty of their own, they just require you to score a point or two more over whatever your Difficulty for the attack normally is. If your stunt affects one opponent, it's generally -1, but if it affects more than one opponent, or is extremely tricky, then it might be -2.
The advantage is that you accomplish more with stunts. For example, shooting at one mook with your gun isn't a stunt, and if you hit, you've just taken out one mook. But, if I declare that I'm, say, shooting the support pole out from under an awning, causing it to swing down and hit four mooks at once who are standing under it, that's a stunt. I may have a -1 or -2 to my Gun AV, but if I hit, the awning smacks four mooks instead of one. That's the advantage.
2. If an attack roll meets or exceeds the Difficulty, it succeeds. So if he attacked you, and tied your Dodge score, you were hit. (I'm assuming this is what you meant by "his AV equaled my own.")
3. Active Dodges set your next action back by one shot. So in your example, if his next act was on shot 10, and you attacked him on shot 13, he could actively dodge, but then his next action wouldn't be until shot 9 instead of 10. (So, you are correct, yes.)
4. The advantage of rolling positive dice is that you succeed better. If I kick you and I roll one positive die and get a 4, but my negative die is a 2, then I've only got +2 total to my martial arts AV score for the attack.
If I roll two positive dice, getting a 6 and a 4, now my -2 on the negative die still leaves me with a +8 total to my AV. Eight is clearly better than two, meaning I have a better chance to hit, and will do more damage when I hit.