Can I use Apple TV to put on TV shows that I recorded on TIVO. Also, can I transfer movies from DVDs to Apple TV. Finally can I transfer movies from my mac to Apple TV. Thanks for your help.
For your first question, Tivo Community may have information on that.
To get DVD's you own to your Apple TV a good start would be to read how to get them to your iPod. The method is pretty much the same, just different automatic setting in Handbrake. There is a guide here. If you are big on having 5.1 surround then I would wait until Handbrake 0.9.2 which is supposed to support that. The guide looks somewhat old as the current version of Handbrake (0.9.1) has presets where you just select "Apple TV".
You cannot (easily) store movies solely on your Apple TV. I have read that removing the file from your computer but leaving it listed in iTunes will leave it on your Apple TV but I would do this at your own risk. An iTunes update may force a re-sync with your Apple TV and lose it all.
With Tivo2Go (part of Toast 8) you can pull recordings from a Tivo to your Mac. Then you should be able to use VisualHub to convert to Apple TV format. Import into iTunes and sync/stream away!