Is moving apps to SD only available to rooted devices? Can I move any apps to SD?
Is there a specific version of Android that I should run: 2.1, 2.2?
Should my phone be rooted for that? Or does it work for stock versions too?
The app has to support moving to the SD card.  
The feature should be in Android 2.2+.  
Your phone doesn't have to be rooted in order to do it.