The rule in iTunes is, if there's a check beside a song, it will put it on the iDevice, or stay on the iDevice if it's already there, if you un-check the box, it will not be put on the iDevice, or if it already on the iDevice it will be deleted from the iDevice. And yes, it syncs from iTunes to the iDevice always. You can delete anything you want on the iDevice and the next time you sync, it will be replaced on the iDevice.