I think you could get the telly put over the fireplace. Might need a mantle to deflect radiant heat, not sure. But on the cables and power, I imagine they can get that sorted. Im guessing there is a wall behind you when you took the photos. I agree that a low corner modular sofa would look great. Just don't get it so long that it is up against the fireplace wall. Placed into that corner of end and piano walls . Then pop your cute chair where the sofa is now. Large ( big enough for the sofa front legs sit on it, I'm guessing 2x3m or even 3x4m) patterned rug to define the area. Can you move the piano to another room or against the computer area wall? Can you make the small windowed room the homework hub? Imagine a long bench against the window ( Ikea do a good cheap range that you make to fit your space). Ensuring the computers are in line of sight from the kitchen(?). Pull out the table to give it more space around it. Or flip it to run the other direction. Hard to tell from the pics the dimensions. Paint a lighter shade as mentioned before. A sketch of your floorplan would be really helpful :)

I think the problem is actually not so much the shape of the room but the fact that at the "pitch of the roof" part you have a large full length window and fireplace. Essentially, because of all this there is no wall to put your back against or place furniture against. My rectangular room has similar issues with a corner window facing the fireplace. We just put the kids toys there on the floor and low kid size stuff like a toy box. You can't put any large pieces there. So, I say, start by completely ignore the top triangle of the room. Its essentially dead or unusable space, but will add to the feelings of space and light in the room. Arrange your large furniture pieces in the bottom square portion, around a large square rug perhaps that would define the space. It might feel better that way. Then arrange your other bits around that. I think if you try to work the square it will be way easier to organise the room. Emphasising a square layout will feel more comfortable. Plants in that light bright corner was a good suggestion, they soften the angles. Hope that helps!

Your island could create some issues near the outer wall. If you move plumbing it will add a lot of extra. Could you put benches around where the kitchen window is and along the back wall, and have the cooktop on the island? Bump out the dining room wall going out to the covered deck and replace with sliding/stacker doors so that it's the same depth as your kitchen. Keep your idea of knocking out the wall between the dining and lounge and keep the door in the kitchen to reach bedroom 3 where it is - or open it up a bit more to really pull together the open look which will cut down the foot traffic you'll use to get to bedroom 3. Blocking air from the front door isn't a problem as you'll have a bigger set of glass doors at the back and the front window in the lounge will create plenty of cross breeze and the front door to kitchen windows.

Wow! Love everything you have done. Kudos to the demolition of extra bedroom in order to reclaim the outdoors. Great job.