|MadSci Network: Astronomy|
You're right: when we see an object, we are seeing that object as it existed at the time it emitted the light we are now seeing. This is true of anything: stars, nebulae, the Sun, a table lamp. Light in empty space travels at a fixed speed, 300,000 kilometers per second, so the further the object happens to be the longer ago the light we are now perceiving was emitted. Other Mad Scientist posts have addressed this kind of thing (see here, and here) in reference to cosmological events, but the same concept remains valid even for nearby things. Of course, a look-back time of 8 minutes (which is the case for the Sun) probably isn't all that profound; it's even less so for the look-back time of a couple of nanoseconds between your eye and the screen of your terminal.
Much of what astronomers so is make predictions about what the objects we see now are going to do in the future: the positions of the planets, expansion of nebulae, and so on. The difficulty is that for most of the things you ask about the amount of time needed for a noticeable change to occur is very long, not only relative to a human lifetime but sometimes relative to the lifetime of the human species. Some nebulae can be seen to expand if you watch them with good instrumentation for a couple of decades, or perhaps less if you get a really favorable case. Predicting supernovae is much harder, because supernova precursors don't show at their surface many signs of their impending doom. We know what kinds of stars explode as supernovae, and there are number of good candidates for it, but whether the light of their explosion is going to reach us tomorrow or in a hundred thousand years isn't something we can say. In the long run our predictions may turn out to be good, but very short-run predictions like that are impossible to make with any reliability.
Try the links in the MadSci Library for more information on Astronomy.