Please do yourself a favor and get a real water well person out there ASAP. I simply do not understand why people get plumbers out to do a job that they are underqualified for. You would not call a plumber out if a light switch wouldn't work or an electrician out if your toilet was leaking, so why would you call a plumber out when you have a well/pump problem? You could have probably already saved enough money and heart-ache to pay for the cost of the true pump guy.
To answer your question, I'm not aware of a submersible pump being able to run backwards unless it's 3-phase, and even then it will still pump, albeit much less water. I seriously doubt you have a 3-phase, but you may have a 3-wire pump, which is not the same.
It sounds like the pump was not installed correctly and the check-valve is leaking back into the well, which causes your pump to cycle rapidly because you are losing the pressure back into the well. It should be an easy fix. I'm not sure if you've had a lot of trouble with wire rubbing the casing and shorting out, but it sounds like it. I know a lot of people who use black-poly pipe have this problem, which is why I always use sch 80 PVC pipe or steel galv. pipe and I never have this problem.
Good luck on fixing your problem.