Your drawing makes your description easy to understand.
I suggest:
- Move the coop south so that each end protrudes out from your run area (6" or so) so that rain falls outside of the run, if needed contour the ground so rain runs away from not into the run.
- Align the west side of coop with west end of the run.
- If you do not want to lose that much run space elevate the coop 3' up using 4" by 4" wood posts.
- Put your coop door on the west side, if you elevate build a small step+landing.
- Put your pop door on the east side for chickens to come go.
This orientation gives you southern exposure for both run and coop.
I believe you plan for a covered run. I would be very careful when you install the hardware cloth to ensure predators cannot get in (I did this and leave the pop door open 24/7, greatly eases your morning & evening responsibilities).
As for your collection of materials, everything looks very usable to me. Your goal is protection/secure place to sleep and paint can go a long way to make mis-matched boards look uniform and attractive.
There are other critical issues such as perimeter aprons but you can sort those out once you design is set.
Others may chime in with their ideas but as far as I can see you can proceed with a Woods Coop given the space and orientations you have to work with.
Keep asking questions folks are happy to help.