Yes
Planets, Moons, Minor Planets can and do have satellites
It gets better... based on these properties of orbital dynamics Tom Van Flandern, an expert in orbital dynamics,
predicted the existence of asteroids having satellites (orbiting moons).
http://www.worsleyschool.net/science.../withmoon.html
Some reading on Hill sphere will aid you with regard to orbital possibilities.
http://en.wikipedia.org/wiki/Hill_sphere
Yes, the moon can in theory have a satellite at around 50-60km hill's length (sphere)
Bonus point - Evidence is pointing this way
http://www.newscientist.com/article/...oon-rings.html