There is no iPod app on the new iPad. The app is now called the Music app. You cannot delete the Music app and you were not able to delete the iPod either so the app has to be on your iPad somewhere.
If you have downloads waiting in iTunes - even if you do believe that you deleted the Music app - you have to finish those downloads or delete them or else your apps will not update. You can only download one thing at a time and the stalled downloads in iTunes are preventing the app downloads and updates from completing.