Heh, I've heard this many times. I actually have no side on this, though I wonder about it sometimes. As for the apperence twin, many of us have seen another person that almost looks like us. Or at least someone that we know has told us that. So, that part is kinda true.
But what about personality and apperence? I honestly don't know. There's so many people out there that I have no speculation on it. But there's always a possiblity.
Final thought, I don't know, but there's a possiblity. It just might depend on what type of twin though.