yes.
The only difference is color, so yes, you can use a regular controller with elite console
No.
No, you cannot sync an Xbox One controller to an Xbox 360. The two controllers use different wireless protocols and are not compatible with each other. If you want to use a controller with an Xbox 360, you will need to use a compatible Xbox 360 controller.
The simple answer is you cannot connect a wireless controller to a PC with just the recharge kit, you will need to buy a wireless controller dongle, or a wired controller if you wish to use an Xbox 360 controller on you PC.
If you have a corded 360 controller just plug it in! If you have wireless you need to buy an adapter.
of course why wouldn't it be!
The black elite controller will work on any model of xbox 360
Yes
Yes, I Use Rechargable Ones :0
The original Xbox controller doesn't work on the 360.
No, The Original Controller and the 360 one have different ports, so you cannot Use Original Xbox Hardware For 360
The Xbox 360 controller will not work on the Xbox one. You will have to use an Xbox One controller.