Thermodynamics is a theory of macroscopic systems at equilibrium and therefore the second law applies only to macroscopic systems with well-defined temperatures. No violation of the second law of thermodynamics has ever been observed in a macroscopic system. But on scales of a few atoms, the second law does not apply; for example, in a system of two molecules, it is possible for the slower-moving ("cold") molecule to transfer energy to the faster-moving ("hot") molecule. Such tiny systems are outside the domain of thermodynamics, but they can be investigated using statistical mechanics. For any isolated system with a mass of more than a few picograms, the second law is true to within a few parts in a million.[2]

2. I think the liquid helium II behaviour is almost equivalent to capillary action with for example water. The helium example being much more impressive since there is no friction between the atoms and no thermal activity so you can view it like an idealized capillary flow that can be explained with Van der Waals forces where each atom just finds the position that requires the least energy.

5. Macroscopic molecules with more than 100 atoms generate interference patterns when passed through gratings one by one. So something interesting is going on. No one can say exactly what happened to the molecule on its way but there are mathematical models that give the correct predictions of the behaviour and there are more than 10 different interpretations of the models. Neither of them makes sense as reality in the normal sense.

1. I don't know much about this but I guess you're asking about what happens if you push electrons to the very extreme of compactness. If you keep "pushing" the electrons together (however you do this), you're really packing a huge amount of energy into a small space (as momentum uncertainty keeps rising), essentially creating a quantum black hole. You'd need a theory of quantum gravity to explain this so I suppose the ultimate answer is, "No one knows."

Surprisingly, this function doesn't drop straight to zero in the "forbidden zone" (where potential energy is higher than particle energy), instead it drops exponentially (more rapidly the higher the boundary). It's like the wave function leaks into any finite boundary.

Due to my awkwardness in maths I stick to practical and thought experiments, like floating gate mosfets and field emission which apparently work well.

Whether objects heavier than the Planck mass (about the weight of a large bacterium) have a de Broglie wavelength is theoretically unclear and experimentally unreachable; above the Planck mass a particle's Compton wavelength would be smaller than the Planck length and its own Schwarzschild radius, a scale at which current theories of physics may break down or need to be replaced by more general ones

Bjorn, are you implying that when box is opened, we would find the solid object unchanged, as it was, but on completely random location?

But what does Compton wavelength mean for macroscopic objects anyway?

Yes, but the larger the object and the shorter the time, the smaller the uncertainty is. The same applies to the ability to tunnel through walls.

The object and box would react to gravity so they will be in a free fall as long as the experiment lasts so it would not matter much what side of the box it comes out.