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.
Log-in in to your iTunes account on your new Mac and then sync as normal. You'll be asked if you want to copy stuff from your iPhone to Mac (which you probably want to do) and then you should be able to continue as normal. Remember to authorize your new Mac with your iTunes account as well.