No, it can only be used with one computer.
There is a useful ipod transfer tool for you to use, iPod to Mac Transfer is specially designed for Mac user to transfer iPod files, It can fast transfer, rip, copy and manage your music, video, photo, podcast and TV program from iPod to Mac, iPod to iTunes, iPod to iPod and Mac to iPod transfer is also available.
Yes you can
If want to put DVD movies on iPod nano, you can use Aimersoft Mac DVD to iPod converter: http://www.aimersoft.com/mac-DVD-to-iPod-converter.HTML
No, you do not need a Mac to have a computer work with your iPod Touch. You can use any PC that has the ability to run iTunes to work with your iPod Touch.
iPod compatabilityYes, it definitely is. Download the iTunes software free from the apple website and you can use it on Mac or Windows.
you use it
No. However if your iPod is formatted for Mac and then used in Windows it may have to be restored before you could use it in the second computer.
Yes, you can still install the iTunes/iPod software, and plug in your iPod, if you have a PC. I have a PC and an iPod.
No as of 2011 you can only use it with a Mac or IPod Touch/ IPhone 4
You can use FaceTime on a Mac to chat with an iPod Touch (See links below).
iChat is not an available feature on the iPod Touch. There is facetime for the new iPod Touch (fourth generation), but iChat is strictly for Mac laptops and desktops.
To use Skype on a Mac product, it must first be downloaded. To download Skype, visit their site and click on the download link. Once downloaded, launch the product and follow the instructions to set it up.