Here's a way to add some orange, but cool it a bit with contrasting blue. You want a rug a 2 feet or more wider than the sofa. Since all the spaces are really just one, match the table and chairs to the TV stand. You can reupholster the dining chairs to work with your color scheme, so don't worry about those when shopping.

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Lower that art to center 5' above the floor, but start shopping for larger, brighter art for there and above the sofa.

Fantastic sofa! I wouldn't add a rug on top of your carpet, but that's my personal preference. I would keep the sofa the star of the room and bring in white and light wood furniture (not so much black) and a more modern style. Add a bit of drama with dark walls.

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I wouldn't use a rug in both spaces - you don't have that much room. Since you have white carpet, I would put a rug just under the dining room table. Find the table you like first, and then shop for the rug, so you will know what size to find. I would look for a rectangular table, or a round table that seats 4, with a leaf to use for 6 when needed. The rug needs to be large enough to fit the backs of the chair legs when the chairs are pulled out. Then look for a narrow coffee table to use in front of your sofa and large artwork for the wall behind the sofa.