If I was doing it, the wiring would run with the hinges in some nice wire loom. Not the cheap plastic stuff. This stuff,
That way, if you do see some wiring, it look half decent.
I would most likely rebuild the rear of the door as well so it looks pretty/clean when open.
You could reuse the existing leather when finishing the front side (the side you see).
It's been a long time since I sourced out a monitor so I couldn't really help as far as selection goes. I haven't bothered to measure things out either. You or your fabricator can do that.
Labour anywhere from 1-3 days depending on fabricator experience and how it's finished. For example, making a new back side and finishing it like factory, different options for the front side such as fibreglass painted an accent colour or to match the vehicle colour, leather, carbon fibre, etc.