However you hang it, keep in mind that once the sheer fabric falls in front of the back fabric, the sheer will change color. So, let’s say you have pulled back the thermals, but not the sheers. Where the sheers hang over the stacked back thermals will not be the same color as the rest of the window. It doesn’t sound like a big deal until you see it. It is very obvious.

Generally a sofa faces the TV. Not sure if the room is open at the end where you are standing or if there is a door or wall. You could even use the sofa as a room divider where you are standing and leave a walkway behind and on each side for traffic patterns. I would either mount the a TV on the wall it's on, or find a TV cabinet to enclose it that fits the space. Ballard Designs catalog has a shallow one that doesn't take up a lot of depth. I prefer to hide TVs in cabinets unless that is the only purpose for the space. Mounting them and having them in open shelving makes them dust magnets especially since the electrical charges attract dust. The draperies are pretty heavy and a lot of them. I think the room would look more updated and less claustrophobic with possibly shutters, that could also tie in with the ones hiding the opening on the adjacent wall. If using any fabric at all, I'd use only a valance but the draperies are too overpowering. The fabric on the valance could be repeated in throw pillows on the sofa or an ottoman used as a coffee table.

I would wait for the rug, until you have the shutters up and your furniture placed..it may take on a character of its own and you'll want to compliment. My first thought though was to coordinate with your kitchen and incorporate some black, with a black/beige stripped rug, which would be fun with the wallpaper and perhaps paint your chairs black, add the shutters and you could paint the window trim black and add a large black chandelier.

I grew up with these panel doors and remember the glorious day they were replaced by a curtain. So if you are open to the idea, for ease of use, least effort and cost that's a simple fix that your daughter may want herself. The top cabinet doors can be considered a cornice for the drapes, and can be upholstered, maybe in the same fabric as her window curtains, and a simple drape with coordinating stripe on the bottom. Search "upholstered doors" on Houzz, and you will see ideas for nailhead trim, tufting, etc as well. You may also be able to add thin trim molding in a custom design to make them special. Good luck!