Which Apple TV generations support the use of AirPods

Are you in Canada by any chance? The MD199C/A code seems to be for the 3rd generation Apple TV in Canada, whereas the -LL/A code is the part number in the US. I'm not aware of any differences between the two (other than the limitations on Canadian iTunes, such as more limited iCloud TV/Movie accessibility).

You can verify these numbers by adding the Apple TV to your cart in the US or Canadian online Apple Stores.

Yes, the iPhone 5 and newer running iOS 10 can be paired with headphones equipped with the W1 chip.

From Apple's website:

Beats Solo3 Wireless is ready to go when you are. They instantly set up – just power on and hold near your iPhone – and then simultaneously connect to your Apple Watch, iPad and Mac*.

*Requires iCloud account and macOS Sierra, iOS 10, or watchOS 3