I'm not sure what your point is; the OP asked about an old tank with N2/O2, and a prankster joked that the O2 could settle to the bottom. Most of us pointed out this simply won't happen in a scuba tank. Your question about whether an undisturbed gas sample would segregate isn't very clear. Under pressure or in a tank doesn't actually matter. If you're talking about a column of gas that reaches from sea level to the mesosphere, then maybe there will be a very slight segregation. But the difference in gravitational force over 1 meter (or even 10s or 100s of meters) is so trivial that entropy and diffusion, (and convective forces) would keep the gases fully mixed to any measurable degree. Also, your point #1 above isn't really relevant. You mention input/output of "energy", when I suspect you really mean "enthalpy". But the controlling factor here is Free Energy, which takes into account both enthalpy and entropy.1. Mixing two common occurring gases eg. N2, O2 does not require any input/output of energy unlike dissolving a solid in a solvent(endothermic eg. dissolving salt in water or exothermic eg. dissolving NaOH in water).
2. There is no interaction between gas molecules of two different gases eg. He and O2. Unlike eg. hydrogen bonding in some solutions eg. acetic aicd which has "unusual" higher boiling point.
3. Gases do stratify by molecular weight in mesosphere or higher.
4. Helium, the lightest molecule, escape from earth for good.
5. I am not talking about gas under pressure in a confined space(tank). It is about FREE moving one.
I repeat that the Lake Nyos CO2 blanket was a temporary (kinetically controlled) situation. Given time the gases did not stay segregated. Entropy won.