I had trouble attaching the photos of the study/tv room. Hope it will work now.

Since the conservatory is so bright, I would use the darker living room for a TV area. Your iron and glass tables are perfect for the conservatory as it should be treated as a sun room. You might consider outdoor fabric upholstery for your two sofas so you can use them in the conservatory. Then you can start with new furniture in your living/tv room. I would suggest a sectional paired with two upholstered armchairs. As for completing the FP, you should replicate the top trim when you do a mantel. You have lots of accessories strung out and they have no visual weight - hang a big piece of art over the FP.. The tall armoire to the left needs to be used opposite the FP as a visual counter weight to its volume. I assume you'll be putting the tv up at viewing level. If you're interested in flanking the FP with built-in cabinetry, that can make a great spot for TV plus storage, and shelves for decor and books. Try soft roman shades for all the windows, even in the conservaory, rather than drapes.

Missed your post of the study, but here's a clever approach to the long window seat.

You say you are getting sunlight from the north - does that mean you are in the southern hemisphere? I would open out the conservatory so it is one room with the living room. Then you need to find a good architect who will redesign your very awkward fireplace. Paint colors can come after you have improved the basic design/architecture of your room.

What a great home! Love it! If you feel your rooms are too cluttered start by going room by room and making a list of what you need each space to function as. That could help you eliminate items that don't belong in that space.

Thank you ALL for your comments. It is very helpful. I have had a lot of trouble trying to find the right position for the sofas, and even though I know that we should not have put the sofas next to a wall, there was no other solution, as the room has two big glass doors facing each other: one to the landing and the other leading into conservatory (2m X 5m). We don't heat the conservatory as it is only used during warmer months (no insulation and lots of windows facing north!), so for that reason we decided to keep the doors separating it from the LR. The view is beautiful, and that is why I thought to face the sofas in that direction, at least until a nice marble fireplace mantle is purchased and the room gets its focal point. The previous owner removed all antique marble fireplace mantles and installed gas heaters, that of course had to go.
The TV that is now in the LR is there only temporarily, until the roman blinds are installed and we have some more privacy from the neighbours. I am very much inclined to go with a cream for the blinds and decide later on the full length curtains. Should the roman blinds be placed all the way at the top of the window frames in the conservatory, and how wide should they be? The conservatory has three double windows, as well as a small window on either side of the wall. Decoenthusiaste, thank you very much for the study photo. It will be a good inspiration for the shelves next to the fireplace. Which will then throw another question at us: what to do with the piano that is there at the moment.