I would place the sofa facing the fireplace either with access to what's behind the draperies or not, and put the tv where the chair is--roughly. On the far end I'd arrange a small conversation/reading/activity area. IE:2 chairs, a table and a lamp or a small activity table with a hanging lamp. Of course, seeing the scale of your new furniture, once you receive it will help. I just hope you have selected comfortable furniture in a smaller scale than what you have.

I love sky blue and want to paint my room, so i think it depends upon choice and likeness

I would use a bookcase unit with closed doors on the lower half and not too high. Wide and low maybe. Closed lower cabinets are great for toys, games and will not clutter. Open shelves tend to get cluttered after a while. When displaying books, use in stacks standing and lying down. Open space between groupings, not all lined up in rows. Add some decor items sprinkled among the books to give the eye a visual break. I would choose a horizontal art piece for the chair wall. Add some art on the long TV wall leaving a lot of bare wall between the TV . and the artwork between the corners of the chair wall and the window wall.

Well, for lack of a better idea, since you find it a drafty little space. I'm assuming the draft comes in on the right? Most of the necessities in the area are located of the left side; i.e. vent, thermostat, light switch etc. What I would do I think is caulk up the drafty spots, maybe even add sized poster board wrapped in batting I covered in a gorgeous fuscia with diagonal grosgrain ribbons every which way covered with a heavy velvet to be attached to the area above & below the window. (Of course remove the drapes that are hanging in there). This for the purpose of using it as a pin-it board for notes. Attach a table height board covered in felt to carry across the full width of the little room. Leaving just enough space for a comfortable little antique desk chair. Paint the back wall a bright cobalt blue, paint the ceiling a silvery pearlescent white. Find a way to attach a clip-on task lamp. And stretch a heavy duty enough wire across the top of the opening and complete it with a heavy doubled velvet drape with a drooping valance. Place a swag with fringe & jewels on it to be closed when not in use. Voila intrigue is yours!