To answer the question as it stands, yes, you can overheat your chocolate and burn it, and that would be my concern if it was not as shiny as soon as you took it out and stirred it up. Usually you can tell because it will start to get a burned taste, but not always.
If it just wasn't shiny once it re-solidified, that's a pretty sure sign that your chocolate lost its temper. You can melt chocolate in a microwave without un-tempering it, and you can also re-temper it pretty easily. I learned how to do that by watching a How to Cook That video from Ann Reorden's website.
Basically, you don't want to heat the chocolate so much that it loses its temper in the first place. So when you heated the chocolate very slowly and gently, you didn't temper the chocolate, you just prevented it from losing its temper.
I usually get my chocolate too hot, though, like you did on your second try. When that happens, I find it easiest to throw another chunk of the same melting chocolate into the hot stuff and stir that around really well until the temperature is back in the proper range. Then remove what's left of the unmelted piece and use your tempered chocolate. This is one of the techniques explained in that video.
The temperature at which your chocolate loses its temper varies depending on the type of chocolate you use. Off the top of my head, for dark chocolate, you want to make sure it's only heated to 85-90 degrees throughout. For milk chocolate, the temperature range is even lower, and white chocolate is lower still.
So it's not a matter of heating too quickly, but of over-heating. And as long as you don't burn your chocolate, you can actually fix it pretty easily if you have a thermometer.