Predictions: at best some incoherent rant that they can but won't do it for some bullshit reason
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Except that is explicitly not what you said. Expanding to fit an available volume is not infinite expansion, obviously.
Firstly, expansion occurs in all directions... Secondly, once expansion is no longer occurring (due to reaching equilibrium/rest/the confines of the container walls), the particles of course would be resting on one another (as they are during expansion as well...)
You seem to imagine that expansion precludes falling - or they are somehow mutually exclusive. Imagine a squished foam ball (or spring) being dropped...
It's not expanding in size infinitely, no, but the particles are infinitely working to expand, as futile as the efforts may be. The particles will never come to rest, especially not on top of one another. Even at equilibrium, the particles are still in motion at an atomic level.
True, as long as the temperature is non zero kelvin.
Same as the first answer. However, conceptualizing the gas molecules/atoms as darting about (aka billiard balls) is only one useful framework. It is not necessarily correct, or consistent with everything we observe. Gas largely behaves as a fluid, and is an alternative useful conceptual framework. Of course, in either conceptualization - constant motion of some sort remains.