Steve,
It's pretty common for engines to run backwards. This is caused by over priming the engine to where it's flooded. The best fix is to get less fuel in it as you prime it getting it ready to start. Most people usually get too much fuel in them as they underestimate just how much fuel gets into the engine when priming it. Yes, you can sometimes get it to start running the correct direction by "blipping" the throttle stick. If you can't get it reverse direction simply kill the engine and try to start it again. No, this usually will not damage the engine.

Hope this helps

Ken