Can you sync mutiple iPods with the sames iTunes library? I would like to keep just music on my iPod nano, but have both music and videos on my iPod touch. Is this even possible?
Just plug the extra iPod's into your iTunes an it will recognise them as being entirely different. You can even have different syncing settings for each of the iPods (e.g. automatically sync only music to your iPod nano, and only movies to your iPod touch).
iTunes is smart like that.
Yes you can. You can read more about it in this Apple Support article.
Yes. You can sync different Ipods with the iTunes in the same user account in the same machine. BUT not the same Ipod with iTunes in different Machine/User Accounts.