Hi -
The best way to learn about what you might do is listen to what composers have done in the past. There are a lot of examples of theme-and-variations compositions out there.
Mozart wrote a theme-and-variations on what I'd call the "Twinkle twinkle little star" melody that is a classic example. Look for Mozart's variations on "Ah, vous dirais-je, Maman".
About your question, you could do *all* of those things, though you wouldn't want to do them all at once if you want the listener to be able to keep up. The trick to a theme and variations is generally to show the listener where you can take the original theme BUT have it still be recognizable.
-Rob