AirPlay Audio works across all Apple hardware that can run OS X 10.7 or iOS 6. AirPlay Streaming is supported on hardware that is capable of on-GPU H.264 encoding. This includes any Mac after 2011, the iPhone 4S, and iPad 2.
Your 2008 MB should support AirPlay Audio but not AirPlay Streaming (pushing video to other AirPlay devices like the AppleTV).
As for the icon disappearing, this is something I'm still trying to figure out and why I am posting. I have a Mid-2015 MBP 15" and just upgraded to 10.10.4 with iTunes 12 and Apple Music. I've come across a similar issue (missing AirPlay icon) when switching between the standard iTunes window and the MiniPlayer. I can quit iTunes altogether, relaunch it and the icon returns. Switching to MiniPlayer removes the ability to select AirPlay playback sources. Closing the MiniPlayer returns to iTunes window without AirPlay icon.
An annoyance yes, but my workaround is simply launching AirFoil from Rogue Amoeba. AirFoil allows me to output any source from my Mac to my AirPlay network.
Can you downgrade to Mavericks? Of course. It should be listed in the "Purchases" section of the App Store (Apple Menu > App Store... ). You can use Apple's own KBase article to make a bootable USB stick.
Hope this helps.