I think your original idea to put the TV on the wall between the sliders was correct. I don't think a TV ever belongs in front of a window. After you move the TV, put the two chairs closer together under the window with a table between them, and rotate the sofa to face the TV. You may have to angle the TV (but not the TV cabinet) toward the seating for viewing, but I think it will be a more satisfactory arrangement for you.

The first thing I would do is switch your light fixture to track lighting. That way you can focus the light onto that wall much like what is done in an art gallery. I also think that may stop the reflection you are getting. I think putting cabinets on the long wall will really close in the space. I would make your red wall your gallery wall. I'd frame everything in white so they "pop" off the wall. The problem with the other wall being the gallery wall is that it's just to narrow. You can't really stand back far enough to see the art.

Paint your house and ceiling first. You are probably asking for trouble if you put the floors down only to paint over the top of them. If you can, remove the tiles in the kitchen and paint just behind the line of the splashback too. Once painting is done replace kitchen benchtop then splashback. I would call the bathroom its own job and do it individually, unless you only need to paint the ceiling and if a tiler doesn't need to be brought in for anything else in the house? A lot of bathrooms now are getting tiled from floor to the ceiling if this is the case, paint the ceiling first, then tile. If walls need to be painted, it wouldn't really matter if you did them first or last, though if you did it first expect to do some touch-ups. I guess if you really wanted, you could do the first coat before tiles then second after... I don't exactly like stopping and starting painting, so I would do the walls (if they needed to be done) in one hit, after its been tiled. Well that's the order in which I would do everything... Really, for what you're asking, the painting could be done at anytime, but to make life easy on yourself, I would definitely recommend doing it before the floor.

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!