Amp meter shows overcharging

Like everyone says, could be lots of things, but try the simple stuff first.

Could be a sign of a failing battery. Borrow another battery if you can and swap it Problem fixed? If not, you need to dig a little deeper. If you have a voltmeter, start by measuring the voltage across the battery terminals and run the car thru the various conditions you described. Post the results and I'm sure you will get some help.