Without matter - Would black holes dissapear?

I wouldn't call it 'feeding on' - the black hole doesn't need them, and it's not hunting them out. Stuff simply falls 'into' it through gravity, and not very quickly at that - the galaxy is not in danger of being sucked 'into' the black hole. It's theorized that black holes will eventually evaporate under Hawking radiation, but this hasn't been observed - it would take a very, very long time, especially for such a large black hole as we have at the center of our galaxy. Yes, everything that falls into it makes it bigger - it's all being crushed down onto the surface of the dead star with immense density. No, black holes don't move unless the star they formed from was already moving (like in the orbit of a galaxy) or they interact gravitationally with something, like every other star. Black holes aren't actually holes, just very dense, dead stars - everything falling 'into' them becomes part of that star. We can't take pictures of the black hole itself - it's black, and so is space, and it's not emitting radiation. We see them through their gravitational interactions, and from the x-rays emitted from superheated gas falling into them.