Orbitals are distributions, charge density clouds. They are smeared across the entire universe, but their density peaks in the vicinity of the nucleus, and away from its maxima it rapidly decays to almost nothing.



In any case, this doesn't say anything about measurement.

To expand on Cat's response, some orbitals have 'nodes' where the probability of finding the electron in that orbital is zero. However, the volume these nodes occupy is also zero, so in practice you can find the electron in any finite volume of space, however small.

Yes. So a lot of math at that level is abstraction. Its "good enough" for many of our purposes, but its not exact.

Quantum mechanics presents a special problem. You see, to measure something we bounce one thing off of it, and read the result. That's the way light and sound work. As long as the thing you are bouncing is small enough, it does not significantly impact what you are measuring.

At the quantum level though, we are actually shooting enough mass and energy at the thing, that it alters the state of the thing we are observing. Combined with the fact an electron is more an abstraction then a particular spot, it leaves us with the uncertainty principle.