I don't see any reason not to do it. I did this, put darkening shades set in the window and, over that, put tan honey comb shades plus drapes on the outside of the frame extending a bit. That was ten years ago and still look amazing.

Don't think you can do drapes on the doors themselves & have them open. Nor can you do drapes up/over/around the doors & still have them cover the space + stack on the side. I would consider a outside mount Roman Shade all around.

Absolutely. Honeycomb shades on the side windows with drapes mounted above the door is totally acceptable. We see it often in our area. I would try and coordinate the color of the shades and drapes so they compliment one another but besides that, I would say you are good to go.