No, it's not. Unity 2 used a different extension compared to Unity 1 and was not compatible (.unity3d compared to .unityweb). The Unity 3 webplayer is not backwards compatible with Unity 2; if you play both Unity 2 and 3 content you will be using two different web players. However, this is handled automatically so most people probably won't really notice.

Yes, it has to be. They wouldn't release a new version of it that "broke" previous games that worked before. That would be like Adobe releasing a Flash update that made all "old Flash" not work, and that just isn't going to happen.

Edit: For continuity's sake, the answer is actually "no", but the player switches itself between v2 and v3 automatically, so it doesn't matter. I don't know about v1, I'm assuming not?

@Eric5h5 Hello! Thank you for your answer! What do you mean by "this is handled automatically so most people probably won't really notice"? I have a .unity3D 2.x file that do not work when I have only 3.1 player installed. It works, though, if I have the Unity engine 2.x installed, but this is just for me. Everybody else installs just the webplayer. How can I make webplayer 2.x and webplayer 3.x to handle automatically backward compatibility?