Construction can refer to all types of building, often with the idea of building an entire project from the ground up. Erection is used more in the sense of making something upright. Installation is when something additional is added to a building or a room, e.g. a new bathroom installation, an installation of a new shower and bathtub in the bathroom, an installation of new windows, etc.
Mounting is usually when something is attached to an existing wall, e.g. a mirror was mounted on the bathroom wall.