Is Thunderbolt backwards-compatible with mini-DP for both input and output?
Your existing Mini DisplayPort cable (VGA adaptor, etc.) should allow your Thunderbolt equipped MacBook Air to connect to a projector (assuming it worked previously with a Mini DisplayPort output) but, as with all things presentation, you'll want to test the setup in advance if possible.

According to Apple's specs, the  Thunderbolt Display requires a:


  Thunderbolt-enabled Mac computer, including MacBook Air, MacBook Pro, Mac mini, and iMac


Your existing Mac Pro can't use the monitor.