You can put the TV over the fireplace, not the best situation but the way the room lays out it is the only logical place to put it. If you could you should add one additional layer on your mantel that could extend it out another 4" to deflect the radiant coming from the fireplace. I would also mount it on a slimline mounting bracket and have the bottom of the TV no further than 4" above the mantle. Ideally you want the TV to be in as straight a line as possible with your eyes. You don't want to look up too high at the TV, it's like being at a sports bar. Also if you can snake up the power and the HDMI from the cable there is a box they make that has both in one so it makes for a very clean installation.

I would suggest you take out the cabinet that is to the right of the stove and use it elsewhere in the house -- perhaps in the bathroom or dining room with a hutch above it. Then, I would suggest you have someone install a lazy susan cabinet in the corner between the sink counter and the stove, meaning you would move the stove down a bit and have a small cabinet/counter top to the right of the stove. I would suggest you have the cabinets refinished in white and then paint the walls a pastel you like. If you would prefer white walls, then add white-painted crown molding and paint the ceiling a light neutral blue, such as Sherwin Williams Niagara Falls Blue. Then, I would suggest you choose a favorite accent color and use this sparingly in accessories like towels, pot holders, small vases or floral arrangements, and a valence above the triple windows. For a genuine 1940s look, you might have white ceramic square tiles with a rectangular red border installed as a back splash behind and above the stove. If you are replacing counter tops, I would suggest a light color such as white with a beige or light grey vein or striation for some sort of pattern. You might be able to find the same color and design in floor tile OR opt for a wood floor as another poster suggested.

Good that the heat/air system is over the door and doesn't interfere with your decor too much. It appears the ceiling fixture to the right of the FP might indicate that the dining space is there. Put a sofa in front of the FP and two small accent chairs with it, facing each other over a round glass coffee table. Can you wall mount the TV left of the FP? I think the room is too narrow to put the TV above the FP - you'll strain your neck. If you mount it opposite the FP, a sofa and two chairs could work but will need to be small scale - try apartment-sized seating. The sofa could face the window with the chairs opposite it. You could turn to see the fire or to watch TV. Swivel chairs come in handy in such tight space.

An outdoor room is like any other room. First decide what you want to use it for. For example, my back yard has a couple of rooms. The "dining room" is a table and 4 chairs under an inexpensive ($150) 12 ' X 12' Home Depot gazebo . The gazebo gives a pleasant feeling of enclosure and privacy when we sit at the table, and it also keeps the table clean and dry. We have a big hydrangea shrub right at the edge of this area to mark its edge. It's pleasant to sit so close to something blooming. The "living room" is 2 comfortable chairs and a love seat around a coffee table. We entertain there and pull the dining room chairs over if there are more than 4 of us. We also sit there to read in the evening. There's a smallish tree right beside it so it's pleasantly shady. The "kitchen" is the grill and a small table to set things on, and is closest to the kitchen door. Once you have decided how you want to use the space, you'll need to decide whether you want a new "floor". We have a low L-shaped deck that has the three rooms. Or you may decide on a concrete or slab patio for all or part of it. Farther from the house is some grass, and then more big shrubs (evergreen and blooming - little maintenance). And a little raspberry patch because it's fun to eat them right from the bush. The landscaping really comes last, once you have decided on the functions of the area. Don't start planting without a room plan. You may want, for example, to put one of your rooms right against the fence or wall, and if you've already planted shrubs or made beds then they will be in the way. You want to plant trees and larger shrubs so they are useful as the walls and roof of your rooms. Be sure to check the mature size of your plantings (it's on the tags) so you don't end up with branches hanging over your roof or over your neighbor's property. Don't make the mistake of putting in so many beds or plantings that you don't have time to sit and enjoy. A few low-maintenance shrubs that are planted close to where you sit are just as enjoyable as big swaths of flower beds that need weeding, annual bedding plants and maintenance (unless gardening is a hobby that you enjoy spending time at.) Enjoy your new home!