No, the Charge Link for Xbox One™ will not fit the Xbox 360® controller.
The LED on the cable will be orange when the battery is charging and turn white once a full charge is reached.
Compatible batteries include those from the Power Kit and Power Kit Plus. You are also able to use the batteries from the Microsoft® Play and Charge Kit.
Yes, you are able to connect an Xbox One™ controller to PC using a Charge Link cable.
Yes, the Charge Link cable will allow you to power an Xbox One™ controller without a battery.