This is a structural evil that you will have to live with. But there are ways to turn it to your advantage. You could add a false ceiling between the beam and the far wall (about 6 " or so above the height of the soffit (bottom height) of the beam. As an extension of the false ceiling, you can also add a matching fake beam on the far wall side. Then recess lights into the false ceiling. In this way, you can turn this portion of the ceiling into a feature. With this feature, you could also turn attention away from the upturned 'pit' portion between the beam and the far wall. A fake beam at the far end will not interfere with circulation space, since you could place an entertainment unit there As an alternative to the false ceiling, you could create shallower beams in wood in that portion, parallel to the existing beam

I would go with large canvases to keep the walls from getting too busy, I think there is enough going on with the bookcase in this space. I also like sections dropped asymmetrically for interest with some lighting and color to accentuate the ceiling. I love clouds painted on bedroom ceilings.They give you freedom to go with stunning lighting that would not fit in conventional spaces. I like to have my eye drawn up, when we visit Europe I think I spend a lot of time looking up at some amazing ceilings.

and about the led light In talking about a single piece doing both fixed illumination and movable illumination simultaneously . in other words how can I get this effect seen in this picture

There are two option one use masking tape to mark the area and paint black and cover light in masking tape, second option take 4 inch or 6 inch mdf duco paint and fix in pop ceiling use black screws to fix the mdf