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.

Medicine cabinets have come along way in recent years. The best option is to get a frameless style and integrate it into a wall of mirror. You can mount sconces thru the mirror on either side of the cabinet. If you have walls on either side of the sink, you can put the cabinets to the side, integrated into mirror again. If you have an open wall in your bath, yo can get an extra tall medicine cabinet to hold loads of stuff. There are loads more on houzz photos. Just search medicine cabinet. Sometimes you have to hunt for the cabinet because they are so well integrated. Robern makes some of the best frameless styles, but there are a ton of others on faucetdirect.com. Many even come with integrated lighting for a very modern look.

If you are going to the effort of retiling the fireplace surround, would you consider going to a bit more effort and creating a full wall unit which incorporates the fireplace and the TV, with extra shelves and cupboards to display and store? (I also have reservations about the heat and the TV and associated wiring.) This may also address the lack of symmetry associated with the location of the fireplace, if that is a consideration. Do you use the fireplace often enough to justify keeping it? Alternatively, a wall unit on the left hand wall, which is where the power and TV points seem to be, may be the best solution - as previously suggested. All the best.