I think a comfortable distance between the island and the counter is around 42". It seems that you have only 30" between your cook top and the counter. I might be a little too tight. The wall between the entrance and the kitchen could be 4' long instead of 6', you would then be able to move the island a foot which would give you more room between the cook top and the island. Could you switch the location of the toilet and vanity in your dad's bathroom so your enter facing a vanity instead of a toilet which is a lot nicer.

Given your space constraints, I think it would be best to hang the TV on the wall that is common to the study/living room (just to the right of the door entry). You could get two or three small upholstered chairs for the living area (gives you flexibility in moving them around.) I would have a table surface hung so it can swing out and be used on the wall between the door and the opening to the kitchen. If hung with a hinge attachment so it can be flat on the wall when not in use, you still have space to move around. Backless bar stools could be lined up on that wall when the table is stored flat to the wall, and still be used for more guest seating.

In that space you will only really have room for some seating and a DR table and chairs I would be looking fo a long low shallow unit for the media pieces and hang the T.V. on the wall 10.5 ' is very narrow. The room in these pics is almost exactly the same size as yours , if you see where the empty fireplace is that is where I would put your T.V. and then wap the bench for the sofa .

For the dining room, I think I'd orient the table 90 degrees from how it's drawn, and I would make it a drop leaf or gateleg table so that it can be made smaller when not being used for dining. I would embrace the idea that the entry is right in the middle of the living room, and bring the living room furniture out towards the fireplace so the fireplace is connected to the seating area. Maybe TV above fireplace. In that back corner where the sofa is drawn, I'd make that a small work/office space.