When I was a kid I grew up in southern California. My father used to take us to the 7-11 on the corner for Slurpees and gum. There was usually a display on the counter that sold little clear plastic boxes of 4 or 5 mexican jumping beans. You could hear the display rattle as the beans clicked against the plastic boxes. We would buy them and play games with them on the kitchen table. So, to answer Question #1, mexican jumping beans are real.
Question 1A should be, "Do mexican jumping beans have the near-human mental capacity of the beans that help Speedy Gonzalez? Are they able to jump the length of a room, trip adversaries, etc.?" Unfortunately, no. Mexican jumping beans are about the size of a kernel of corn or a small bean (there's a picture on this page). They do not wear sombreros. They do not jump into the air. They rock, or on occasion scoot a millimeter or two. Imagine a kernel of corn that scoots a millimeter in one direction every 15 seconds or so -- That's about as exciting as jumping beans get.
The thing that makes these beans jump is a tiny moth larvae that lives inside the bean. The moth lays its eggs in the flower of the plant, and the eggs are incorporated into the seeds. The larvae then eat out the interior of the bean and live there. When the larvae move, so does the bean. Eventually the larvae turn into moths that emerge from the beans to repeat the cycle.
Here are several interesting links: