These guidelines will help you get the right size lamps. You already have enough shutters in the room. The headboard is too high for anything to hang above it. Maybe one of the gifted ones on here will put in some very tall mirrors above the bedside tables for you to see, but I think stationary drapes flanking the windows would add just the right touch.

There is no correct answer! We have no idea how tall your ceiling are and what else is in the room. I would take some poster board or even 8-1/2 x 11 paper sheets and tape them up on the wall to mimic the size of the sign. You can then take photos of several options and post them here. People can then tell you which option they think is more visually pleasing.

Yes. And a shelf or long, narrow console table so the sofa isn’t jammed up against the walls. That’s a large sofa. Let it breath. Jammed against the walls it looks like you bought a sofa too big for the room and have shoehorned it in (which isn’t true).

Could the dresser work on the other wall facing bed, so bed can be centred, as you mentioned you like symmetry. When art and side lamps are added it will feel even more unbalanced. In regards to art above headboard, below is a example of 3 prints to help with height and spacing. Another idea is to add prints above side tables. Roman blinds would look nice, per first picture