[siver_john]

Not bad for an armchair physicist. Disclaimer, my undergraduate degree was in physics but I'm not a quantum expert by any measure and my graduate work took me closer to statistical mechanics.

So for the simplest explanation for you and the parent is that as you said electrons are both particles and waves, there are experiments that we can demonstrate for that. But if you're thinking of the electron cloud then that exists partially because you aren't measuring the electron. Basically this particle(s)/wave(s) orbiting the atom can exist in a lot of different configurations at once determined by it's energy (which is influenced by its/they position and how fast it is/they are moving). For educational purposes we often treat them more exclusively as a particle (early electrodynamics) or a wave (early quantum) depending on what field we are talking about.

Of course there is greater definition I can give to what it is if we want to start talking about what protons and neutrons are made of and most of that is what occurs at the LHC. (But I'm heavily out of my depth in high energy particle physics).

The measurement uncertainty applies to some other properties as well basically your uncertainty in the electron's position (sigma_x) and uncertainty in the electron's momentum (sigma_p) are bound by sigma_p * sigma_x >= hbar/2

hbar is the reduced planck constant and sigma are statistical variance, but that condition must always hold so as sigma_x goes to 0 (you are more certain about the potential) sigma_p must get larger to compensate so you are less certain about the momentum. This measurement collapses the waveform and until enough time passes for the system to "normalize" the momentum will continue to be uncertain, after that you can measure the momentum but the position could be different too.