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.

They may have used small dowl rods or biscuits to join the chair. Which usually means a void/rebate is created and then a proud piece glued into the void. (Think male/female sockets etc). So you may be able to gently tap (rubber mallet, not metal hammer) to get the pieces apart. Use fabric or thick wadding or sponge to protect your timber when you whack it.

And the seating areas are different, don't try to make it look like one area. I would put minimal ( if any) teal around the black sofa. Do your dining room. Then give you living room the same respect, it is it's own space

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.