(Not a Teacher)
A cloakroom is a room where coats and hats are hung. In homes that have one, the front door usually opens up into the cloakroom.
1) The closet in which you keep your clothes can also be called a wardrobe.
2) Not sure if there is a specific term for it. Maybe just call it a recessed balcony. Can you stand on this balcony or is it decorative? Decorative balconies are called balconets.
You may have to link a picture.