No, it applies to scattering states. I think this is pretty clear in the text you posted.
When E>0, you will always get transmission, i.e., there is always a non-zero probability that the particle will go from one side of the well to the other. What is surprising from a classical point of...
It appears that you are looking for a simple explanation where one doesn't exist.
Electronic configuration of multi-electron atoms is complex. While in many cases, one can come up with simple heuristics to explain what is observed, there are anomalous configurations that don't fit the pattern...
This is a potential well, not a potential barrier.
But yes, there is a non-zero chance that the particle will be reflected even though E>0. This is purely a quantum mechanical phenomenon.
A much more reproducible experiment would be to take a single pot with a lid with a hole in it, and change the size of the hole. You can take a single sheet of appropriate material (if it's plastic, make sure it won't melt or deform at boiling temperatures) with a hole in it that you make...