songs from ipod to itune

If you move your songs from your PC to another directory, or delete them, after synchronizing them to iPod, you can play them in iPod [because they are present inside iPod], but you cannot play them in iTunes, because iTunes cannot find the audio file on your PC.

[iTunes works like normal PC media player, which plays songs from your PC, from the location they were initially added from.]

This happened to your songs because you must have moved your audio files to some other place, after adding them in iTunes. Now, your iTunes is only showing the list of songs, but cannot find the songs.

If you want your iTunes to play those songs, you need to add them again.
But then, you need to delete the duplicate songs as well.
Or, if you remember, place that audio directory at the location it was initially present.

For your other issue, look for the option "Synchronize only checked songs" in iTunes.
If that is selected, and some of your songs are not checked, they will not be synchronized.

:-)

"If you want your iTunes to play those songs, you need to add them again."
The problem is all of my imported songs are placed in the playlists. So if I have 2000 songs, it will take forever to import those songs and move them to new created playlists.

I did not work. I will import the songs again and backup the two files that you mentioned. thanks