With a jailbroken iPod Touch, you can...
Yes, you can put music on a jailbroken iPod Touch.
you cant
Yes, the iPod Touch with the 2.0 software can be jailbroken.
yes restore it
I guess
Once jailbroken, the iPod Touch's one year warranty is void.
No...
it is battery
Not without erasing the jailbreak.
A jailbroken iPod Touch is certainly legal. However, the act of getting every app in the App Store for free (the ones that require payment) is illegal.
Currently, the iPod Touch 3rd generation cannot be jailbroken because it has a built-in firewall of sorts, a measure taken by Apple to prevent the iPod Touch from being jailbroken. There is a jailbreak software currently being beta-tested, but is not ready for public use.
No, unless you have jailbroken it (in which case it is highly likely).