After mixing... the next step, mastering..

Yes...

With out a dought...

If the ME does not accept each song indvidually then find a new ME. Like Gomez mentioned every mix requires diffrent mastering. Shoot there are ME's I know that say they will do one pass mastering for a deal or they will do it the correct way and work on each song indvidually. An yME should be able to work with just about anything you throw at him/her. If they can't I would seriously be worried about them.

As far as sending the ME seperated tracks of one song (i.e. music / vocals) is concerned (each track is called a stem), this is something that the ME may or may not want. It is basically giving the ME a chance to further mess with a mix after the fact. It is not his job to do this but he might be willing in order to make the Master as efficent as possible. There is a lot of ME's now a days that want stems of everything (i.e. Vocals, guitars, drums, bass).