it's possible with the latest MacOS (Mountain Lion). With this MacOS you can do what it's called a desktop Mirroring. So whatever you see on the iMac screen will be on the TV through the Apple TV; just like the iPhone and iPad mirroring.
Yes. AirPlay and mirroring allows the content of the MacOS and iOS to be displayed on the TV via Apple TV. As long as the unit is loged onto the same home-sharing network, and linked to the Apple TV. Just one thing, though I haven't tried it, I understand that the media has to be controlled from the computer itself. The Apple TV will only provide a magnified display of whatever is on the computer screen.
No, you can't do that LEGALLY. There are third party apps which will allow you to get around this but it is still considered illegal for you to play DVD's that you have produced or bought legally through your Mac computer onto another monitor. Lodge complaints with MPAA.
No, you can't do that with the Apple TV. You could make a copy of the DVD (using Handbrake for example) making sure it is an iTunes compatible format such as .m4v. Handbrake has presets for Apple devices to make it easier for you. Then import the file into iTunes on your MacBook and it will show up in your iTunes library on Apple TV using Homesharing. Make sure you have plenty of hard drive space if you plan on doing this to more than a few DVDs though.