To be honest, to answer all of your questions would take a long time. It's not as simple as a two or three sentence answer. To be honest, it's more of a very long term paper if not a book.
I will answer one of the simple questions though.
What is a solenoid?
A solenoid is simply a electro magnetic relay. It has continuous power to it. It is activated by another power source that is switch activated. When activated, the electro magnet raises a piece of metal(usually copper) to make contact with the constant power source. It will also contact the opposite side of the relay, sending power to the device( ie the winch motor, lights, or anything electronic device). A winch solenoid is as said before, a relay. Very much like the one for your starter.
Hope this helps