I would stick with one story because an accident, disability or aging would make a two story less accessible.

Ditto! Lol. Carpet is much quieter and safer (I've slid down my previous 'all wooden' steps before now!) but I hate it too. If you have good treads, I'd go for a stylish runner which looks nicer. Get a busy pattern ie stripes or funky geometries to keep the dirt less obvious.

This was a very difficult staircase to build but this finish product is amazing

Real or engineered wood would be my first choice in a herringbone style but of course LVT is a much more budget friendly option. Underfloor heating is not easy to fit retrospectively and a lot of upheaval. If your radiators work I would keep them and work around them. I think your fireplace is a bit high to mount the tv over, the pic you show has a lovely round mirror and the tv at a much better height for viewing. Sit on a chair against the opposite wall and see what viewing angle is comfortable before you do that. Can you have a large sofa (3 seater) along the wall opposite the tv? You could than have a snuggler chair or just an additional armchair or two if space is an issue. A floorplan would provide a full background and we could advise you better on layout issues. Your image is lovely. I love the neutral wall colour.