Well, I'll start with the easy ones.
Your files from your windows partition (I'm assuming you have a dual-boot) are accessible from ubuntu with an ntfs driver. After you have that setup, you can easily just access them right off your windows partition to save space, or you can copy them over to your windows partition. The driver you'll need for accessing the NTFS (windows) filesystem is called ntfs-3g.
There are instructions at The Ubuntu Wiki
If you want to save hard disk space, create a softlink to your windows music folder from your ubuntu home folder:
~$ln -s /media/windows/Documents\ and\ Settings\name\My\ Documents\My\ Music ./music
That assumes your NTFS partition is mounted at /media/windows.
For limewire, you could use the linux version of limewire or you could try Frostwire
. Not sure if it's in the repos, but there is a binary package on their site.
For itunes, try amarok.
$aptitude update && aptitude install amarok
Alternately, you could try songbird
, which is still in beta. Like frostwire, that is a binary package. Put it in /usr/local/bin and extract it.
Your internet connection difficulties are difficult to fix without more information. Are you trying wired or wireless? I'd get wired connection up so you can get all the packages you need. You shouldn't need a password unless your LAN is protected. Is it asking you for a password to your router or a password for your ISP? Is your IP and DNS and gateway setup correctly? both Gnome has a network tool under utilities somewhere.