I think you need to go back and reread some of the science again. A black hole is a dead star that has collapsed to a singularity, a single point in space. Its gravity is so great that nothing can escape, not even infrared radiation. Hawking Radiation is a special case, and isn't really easy to detect anyway. We detect black holes by their effect on their surroundings: they are massive, so their gravity affects nearby stars. Like Yoda says, you just look for the center of the attraction, and there a black hole will you find. Also, their gravity will distort the images of stars behind them, and you can look for double-images to find black holes.
Contrast this with a pulsar, neutron star, and quark star. These are all less-massive dead stars that have not collapsed far enough to become a black hole. They can still be found using their gravity, and we can technically 'see' them, although they are very faint... except pulsars, which can be very loud [edit: read 'bright'] at certain frequencies!
As far as whether Black Holes exist: we are pretty damned sure they do. Too many observations indicate that they do, other theories predicts that they do, and the data match hypothetical calculations exactly within experimental error. Science cannot actually 'prove' anything, for philosophical reasons. Black Holes are at a state of understanding that scientists call 'theory,' but that isn't a theory in the way you mean it. To a scientist, a 'theory' is a reliable, usable piece of scientific understanding (what you would probably call a 'scientific fact'). What you call a 'theory,' we call a hypothesis. Black Holes are a matter of theory, meaning they are about as proven as they are going to get. If we are wrong about black holes, we are likely wrong about a whole lot of other significant things. That gives us more confidence, actually, since it means that all of our observations are in tune with one another.
There isn't much else we can do with black holes. If we get closer to them, we can do fun things like observe their tidal effect (your toes will be more attracted to the star than your head, for example), and we can drop things so that they fall forever into the event horizon. We can go around it and look at the gravitational lensing effect from every angle. But there isn't really anything you can do there that you can't already do from here with some effort. So waiting to find out more isn't a very productive idea...
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