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 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.

Considering my house is upstairs, my home would be useless for when I'm old. Absolutely useless. There's no shower downstairs either so I'd have to install one of those elevators that help you go up the stairs.

It all depends on what you want to do in your laundry and what in your bathroom I guess. I appreciate the fact that there might not be enough space to do this but I store outdoor shoes in the laundry and the dog's leash and cleaning stuff. I need room to sort the dirty laundry into piles before washing it. I keep the ironing board in there and I need a tub to wash things in and to do flowers in and to put the odd cloth that wiped up the cat sick before it gets rinsed and washed.. heaps of things other than just washing. Couldn't manage with a cupboard laundry ( piles of washing on the hall floor when using it) and think these kinds of laundry functions might not make a gorgeous lavendery bath or shower feel that luxurious. So I am for as big a laundry with tubs, cupboard and bench nearest the outside back entrance and yes washing line as poss. And a lovely fresh warm bathroom near the bedroom separate from the dirty clothes and boots and all that other stuff.