The entire wall (wood, insulation etc) is supposed to wrapped from the top down under the 2x4s then back up to the top of the interior of the wall, so 2 layers of vapor barrier in a "U" shape. Putting a vapor barrier only on the inside will keep moisture inside the wall if it ever gets in and will cause mold. This was not done correctly.

Space saver

Yep even in New houses there may not be a junction box in the wall because the original light fixture was a "metal box" which was up to code enough.

The door needs to be moved rightward, get a block of wood and a small hand sledge and bang the whole hing set over to the right about a millimeter. (Both hinges) that should move the whole door and hinges rightward fixing your issue. May take quite a few wacks if the metal is strong but they don't look overly heavy duty.

Also no need for a box. Makes no sense.

Hey, I did this same thing not long ago for my Chevrolet volt plug. Use the larger wire only, don't splice it down into the smaller wire the last 2 feet. The wire is thick but it will still bend enough for you to go around corners. Less connections is better. Mine works like a charm, car charges waaaay faster now. I had left over stove wiring, so its oversized truly, but bigger is okay.