Also, suggestions for the area over the door?

What about navy? It will complement the rug and teal accent pieces as well as add some color but it's still sophisticated and acts like a neutral.

I like the door white, but could see a more saturated version of some blue from the chair or rug. Not sure how you can coordinate with the adjoining room, given that the wall paint there seems incompatible with the color of the two pieces in the entry here. If skipping a blue, you could maybe do a charcoal or medium gray, which would make the door stand out without it's dominating the zone...

Nothing over the door -- decorate at human level and leave high swoops of architecture as restful paths for the eye.