Fixing patch in the wall
Looks like the bracket was attached to the molding (?) with a screw that was too short.

Remove the bracket carefully.  You need to salvage the piece of the trim that the screw pulled out - the part behind the bracket.  Glue the trim back onto the molding, then patch with some wood filler, sand, and paint.

Reattach the bracket using a longer screw that goes through the wood trim, drywall (or plaster), and into the 2x4 that should be below the window itself.  Pre-drill the hole so that you don't split the trim.