You should install iTunes in your new computer (here: http://www.apple.com/itunes/download/) and plug in your iPod. iTunes will then ask if you want to sync your iPod to your new computer. About trasnferring music from your iPod to your new computer, iPod and iTunes does not provide that funcionality. There are however ways to do it. You can read one of them here: http://www.ilounge.com/index.php/articles/comments/copying-music-from-ipod-to-computer
When you plug in the iPod to the new computer, iTunes should display a message that reads something like "purchased items have been detected on this iPod. Would you like to transfer these purchases?" this message may display before or after you choose to sync the iPod with that computer. However, it may be risky to sync if the message does not display beforehand. It should display a one point though, and a problem only arises if the message is never shown. Hope this helps and sorry i couldn't provide an absolute answer.
You need to have iTunes downloaded on that computer first. Then you just plug it in and it syncs and all the songs and apps are then copied onto that computer.
No. If you are downloading your computer needs to be on
No
Plain and simple you cant
From your old computer, go to the 'File' menu on iTunes, go to 'Library', then 'Back up library'. Copy the backup, open with iTunes on the new computer, and it should be there.
Yes.
You can't. If you sync with iTunes on another computer iTunes will force you to wipe the iPod.
yes
Yes but if you go into music/itunes and back-up the itunes folder onto a USB stick or something then put it back on your computer once you reinstalled itunes then it should be fine.
When iTunes is upgraded, it preserves your music library so just run the upgrade process and you'll be fine
You can move your iTunes music library from a Windows computer to a Mac without losing any of your songs. (See links below)
If think that this doesn't work because I've tried it before
You don't have to upgrade iTunes, you just can set your ipod touch to a "replacement" even though it's not.