The problem is obviously all those doorways. However, I would ignore them in terms of placing furniture and put a comfortable chair on each side perpendicular to the sofa. As long as the chair is small enough that you can easily get around it it's not going to matter if it partially obstructs the doorway. You want to have a U-shaped configuration so that as many people as possible can watch TV comfortably. You'll also need side table between the couch and the chairs in addition to a coffee table in order to make the room look furnished and so that people can place their coffee cups, dessert plates etc, somewhere. You might want to see if there's enough room on one side to place a small loveseat which can seat one adult and one child to increase seating. I would strongly consider a large area rug to lend some softness and color to this room which has so many openings with the bare windows and three large doorways. This will make the seating area look more finished and cozy rather than just some haphazardly placed furniture. More pillows would also be a good idea to soften the scheme and give it some cohesiveness, with the pillows picking up some of the colors of the rug. Colorful and interesting wall art would be a necessity to finish off this room, with more furniture (bookcases, desks, a secretary etc.) against the walls.

Do you ever use the FP? Is it real or gas/electric? Is the closet built in or free standing? Looks like it might do well in a mudroom/hall. What is inside the bulkhead over the windows? Why don't you move the mirror to the dining room and get a nice chandelier to be doubled by it? Your dining rug is too small. Needs to be 6' bigger than the table so the chairs don't fall off it when in use. BUT it shouldn't run into baseboards or furniture on the walls. Maybe do without it and soften with drapes instead. Can you take a pic standing in front of the TV?

what a great space for him. so many ideas. first thing I'd do is some built-ins in some of those nooks. simple plywood, paint. For books, video games, collections, etc. that inset next to the J would be the perfect spot for a built in bookcase. Look at Ikea hacks, or DIY inset bookcase tutorials. Ikea Billy Bookcasehack: https://food52.com/blog/25110-best-ikea-billy-bookcase-hacks how about a mural (peel and stick) of some sort? you could do it on the wall or on that sloped ceiling above his bed. bring in some sstring lights and drape them from wall to wall do a lower bed like this, back in that corner, string the lights around it, and remove that nightstand, replace w/a cute table. or something like this platform style bed. put on a regular mattress or a futon mattress. do a diff light. remove that futon across from it and bring in a low-boy dresser of some type. bring in lots of thin, cotton dhurrie rugs you could do a roman clay treatment on the wall and paint a dark color. maybe bring in some faux beams from side to side drape the lights over those: for the lower areas that are wasted space, do something like these low open shelf cubbies (enlarge this pic to see them) decor ideas, lighting, bean bags, get some cheap pine tongue and groove flooring (lumber liquidators) and install it on one wall, or on one of the angled ceilings, or around the desk area, behind the sofa, etc what's under that carpet? some type of wood? you could paint it w/porch paint and thrown down a bunch of cool looking rugs. maybe redo the desk w/Ikea desk hacks. you could get a solid piece of butcher block (or a remnant), span it to fit across the entire area under the window, (use cleats to get it to 'float') and then some pull out ikea drawers. or something like this gray one. maybe hang a light directly over the desk, or get a desk light remove that heavy blue drape, and do an inset window blind. I did this black cellular blind on my sons bedroom window. If you get the blackout option, you won't need the heavy drape to block out the light. something liek this. it's less bulky looking, the desk looks better, (frame out the window w/white trim if you're using a dark shade), and the pendant light gives overhead light in that dark space.

This appears to be token living room. There's really only room for an apt. sized sofa and a lounge chair. I don't see any place to mount a TV for this space. What exactly is your definition of wainscotting. If you are planning to add full height strips to the walls I'm all for that as it will visually heighten the appearance of the rooms. A half height is just going to make your walls appear shorter and I would avoid that. The Windsor Hoop back chairs are a bit too 'kitcheny' for this space. Select a chair that either matches or contrasts the table. No turned spindle legs.