If you throw gasoline out on to the pavement it will evaporate away. If you keep it in a gasoline can it will not. In a gasoline can the liquid and gas will reach equilibrium, though you’ll certainly have slightly less liquid than what you started with. If the can isn’t sealed then, yes, all the gasoline will eventually evaporate away - even at STP.

And, again, this is all trivial to test at home by using some hand sanitizer. Another example is your skin does not remain wet with water forever, despite human skin temperature not being 100°C. It’s an everyday phenomena, I’m not sure what you’re trying to argue against here. It’s not my “line of thinking,” it’s objectively reality.

As for your distillation problem, the issue isn’t that some alcohol remains in the water - it’s that some water evaporates alongside the alcohol during the distillation process at the boiling point of alcohol - due to, guess what, vapor pressure. That’s called an azeotrope - clicking through to that Wikipedia page might have helped.