It's not 1*1*2. As I said, breadth cancels.
1. How does "breadth cancels" exactly? You have to explain yourself. The breadth can't be zero, or the volume is zero.
2. You said that it was double as long as it was wide. Width = 1w, then length equals 2w so the measurements of this cuboid is 1*1*2.
And let's just assume that the molecules bounce off 90° from a wall
I justified this assumption.
Not really. You can't prove that they will cancel each other out, you just said they did. And It would be easier if we just assumed that molecules traveled back and forth along the same linear path. It was just a simplification from me.
For air molecules to collide with a side, they must be going in the right direction. In the absence of an external force, this is only possible if they are bouncing off another surface. Ignoring side-to-end and end-to-side collisions (which will balance out), this means there are 2wn molecules heading towards an end (those on the surface times the space in between): there are, however, 4wn heading towards each edge, because there are more heading in the correct direction to collide.
So long as the right relationship holds, that is that the surface area of a side is large enough compared to the width, the pressure we observe will exist.
So, a bit wrong. Towards each side there will be 2wn of molecules heading it's way. I don't know why you multiplied that by 2. So for every end and side, each of them will have 2wn molecules heading towards it (assuming molecules travel through each other without interacting). And then... you just stopped? You have to calculate pressure in some way to prove something about pressure, you know? You have to finish your equations. You have not proved anything yet.