help syncing songs from iphone to laptop

when i purchase songs from itunes on my iphone does it automatically add it into my itunes library on my laptop? because i dont see it happening so i connect my iphone to laptop and it just duplicates the playlist like "jammin playlist 1 ......and i have too many playlists "jammin playlist" "mellow" "christmas" etc, so it duplicates all of them. and when i click on jammin playlist - there are 55songs. when i click on jammin playlist 1 - there are fewer songs.

when having several playlists shouldnt i be able to have just ONE PLAYLIST that has all of my downloads and purchases? or doesnt it do that? PLEASE help! i have so many frustrations over this! THANK YOU IN ADVANCE. Stacey