Most units have a built in mixing valve and the mounting hardware is included as well.

You will need shower curtains or a sliding door mounted to the tub.

No, it does not

The nozzles are in both mist and jets.

All of the controls are metal. The outlets on the spouts and jets have a metal exterior but the inner holes/nozzles are plastic. Most customers are impressed with the overall build quality of this assembly. 

It is powered by AA Batteries. The cradle is located at the bottom of the fixture.

The rainfall shower head is adjustable.

The LED is powered by the water flow. As long as the water is able to flow out of your shower head, you will have lights. So it is energy-saving and environmentally friendly. It is also quite easy to install LED shower heads because it is designed to replace the existing shower head.

Depending on the model. Some range hood come with a rectangular exhaust at the back.

Some are Halogen light blubs and some are LED display

The airflow is the same between the circular vent and the rectangular vent.