Yes, I know what you mean about the symmetry. I was thinking the same but just couldn't make it work. I was even thinking about some sort of recess (just 30mm or so) where the window would be, almost like the window space had been filled in but you could still see the outline. I'm pretty sure I've seen similar before.
Yes, the plot is longer than it is wide and yes, the back garden faces North. As such I guess it is a North facing plot. There is also a couple of large trees at the front of the plot so not a vast amount of light there either.
Yes, true, there is quite a bit of space either way so definitely gives options.