How can I retrieve missing playlists on iPod Touch?

I've just bought a second hand ipod touch 6th generation, as the home button has failed on my 4th generation ipod. I used the 4th gen ipod to play podcasts and music in my car (BMW) & thought the 6th gen would do too. however, there are several issues:

1. I have a playlist on itunes that contains unplayed podcasts. It works fine in itunes but although the playlist shows in "Music" on the ipod, the playlist won't open if I touch the icon. The playlist does not show in "Podcasts" on the ipod.
2. I've also synched the 6th gen ipod with my car and the car display shows all of my playlists - but all of them show empty, including standard playlists such as "top rated".

I'm completely lost on what to do - other than try and buy another 4th gen ipod(!). Help!!!

[Re-Titled by Moderator]