I don;t know about material for awning--my though would be to match the roof. I suggest that you make the new awning wide enough to be symmetric with the peak of the roof. Then widen the door stoop and sidewalk to fit. Perhaps place a bench or a planter in the new area.

The attic louvre isn’t offset, the door is, and there’s no fix for that so living with this little quirk is the best way to go. And I’d do a green and white striped fabric awning, as similar as you can to the other green but even if it’s not the same it’ll look great

I wouldn't do any white on the awning. Maybe black would be best, or a very dark green. Oaks drop their "flowers" and can leave stains that probably stain any white fabric awning.

I love the idea of a copper awning both visually and from a practical perspective and the upfront cost will outweigh the cost of having to replace fabric every few years. Also suggest painting the door and even consider adding vines.