Does the Earth have similar satellites? If so, how many?
Yes, but just barely (i.e. only one so far), and only for the L4 point. And this was only recently discovered. Dr. Phil Plait (an Astronomer) covers this at his Discover Magazine blog in his usual easy to read style.
NASA’s Wide-field Infrared Survey Explorer (WISE) has found the very first asteroid that (more or less) shares an orbit with Earth! Called 2010 TK7, this asteroid is about 300 meters (roughly 1000 feet) across, and is the first in an up-to-now theoretical class of objects called Earth Trojans.