The iPod appearing on your desktop with the red "no access" sign is normal -- that's the icon that the iPod uses when mounted as a disk drive on the desktop. You'll see that if you double-click that icon, you can access the iPod as a regular removable disk drive. If you connect the iPod to your computer and iTunes is not currently running, the iPod will mount as a removable disk on the desktop. Before disconnecting the iPod from the computer, you should eject this mounted icon like you would eject any other removable media (drag it to the trash, or highlight it and press Command-E). Look at the iPod's screen and make sure it doesn't say "Do not remove iPod" with the no access symbol before disconnecting it from the computer.
The iPod will also mount on the desktop if you have "Enable disk use" checked in iTunes' preferences under "iPod" whether iTunes is open or not.
Also, all the tracks on the iPod when viewed through iTunes should be greyed out -- that's perfectly normal. You cannot manipulate tracks already on the iPod -- that's why they're greyed out. If you want to remove or add tracks to the iPod, simply remove or add tracks from iTunes and the changes will sync with the iPod.
As for the iPod not appearing in iTunes, try launching iTunes first, then connecting the iPod when iTunes has fully loaded.
If all else fails, try resetting/restoring the iPod (make sure your music on the iPod is either backed up or present in iTunes -- all data on the iPod will be erased with a "restore" action). You can do this with the latest iPod software, which should be in your Utilities folder inside the Applications folder.
