Basic Intro to Quantum Chemistry. Two Slit Experiment and Bohr Model
As some commenters have stated, this is a complicated topic, and if you really want to understand it you would probably be best to study quantum mechanics itself. Although it's detailed it's also interesting!

However, as to your question, the first thing to ask is what does it mean for an electron to be "observed"? It can't mean just looking at them with your eyes, because then any matter we looked at would suddenly go crazy when all of its electrons change their behaviour. It also doesn't mean just looking in a normal light microscope, because electrons are too small to see in a light microscope. In fact to really properly "see" an electron, we would need to use very powerful high energy equipment. So high energy in fact, it would give the electron enough energy to fly out of the atom it was attached to. After that it perhaps could well fly off like a "normal particle" electron with a Newtonian path.

Now the obvious question everybody then asks is, is there a way to "look at" the electron bound to an atom without giving it so much energy? And the answer according to physics is no, it is actually impossible, to really "look at" a bound electron enough to make it act like a particle, it always takes a big amount of energy. You could "look at" it just a little bit, just enough to find what energy level it is in for example - but as you probably know this isn't enough to stop it behaving like a spread out wave (atomic orbital).

Now as to your question about why it doesn't fall in to the nucleus, you have actually already answered it. Why would it? The earth doesn't fall in to the sun. You mentioned that electrons are very light, but that doesn't really matter. If we hollowed out the earth to make it much lighter that wouldn't affect its orbit. Now the real reason is a kind of "quantum mechanical" version of this argument that I could explain if you like, but it is complicated and really this is the key reason.