I'm not an expert, but here's what I see. Move the cabinet to the left a bit to leave a wider opening through that slanted walkway. Then bring the lamp out a bit and pick a pretty shade, any that you have picked should work out. The pictures one the wall are too small and they are a little awkwardly hung. Either one large art piece, family photo, or mirror, or a grouping that relate. Clear the top of the cabinet. One larger family picture, one tall thing like a vase, and one smaller shiny thing.

Yes an external blind will interrupt that wonderful second story view, if it has to be down all day. There is not a deck outside that window, so a vergola would not be easy to install, unless it is double storey height. A fixed awning may work. But may have to be large to cover the part of window that is letting sun onto stairs. REtractable awnings, may have times, that they can not be extended because of strong winds. I have had good results with window tinting.

What is the best rug, and how is it made?

Maybe one of these dulux colours. With the correct combination of furniture and accessories will look bright and inviting.