I have seen wireless adapters for the 360 controller but if I remember correctly there was a firmware update to the newer controllers (of 2010) that made that not function anymore. I use a wired 360 controller for Windows and it works perfectly
Yes, you can use your wireless XBOX 360 controller for your PC. It is very simple to do and it works very well. There are no firmware updates required, and it will work with current, and future xbox controller models.
This is plug and play. So yea, just buy the receiver, and you are in business.
Also, you can just buy the Wireless Xbox 360 controller for Windows, which is the same thing as your current xbox 360 controller, it just comes with the receiver as well.
Hope this helps!