Sorry, your lack of punctuation is causing me trouble...
At what point are your songs deleted... and from where are they deleted? On itunes, your nano or your shuffle?
You are able to "sync" both devices on the same itunes program. If it asks you to format say NO, as format wipes the memory.
I don't think you can use playlists on a shuffle as it is such a small and basic device.
Instead you can drag and drop songs from your library, or if you have them in a playlist, onto your shuffle, when it is plugged in to itunes.