The weight of the air molecules pulling it down towards Earth and the atmospheric pressure pushing it out into space is at equilibrium.

I don't know what "vaulted" is supposed to mean here (what do arches have to do with anything?) but the relevant principles can be shown by laboratory experiment.

Water in a rotating tank takes on a parabolic shape, due to centrifugal force. It does not magically stay level regardless of what forces are there, it takes a shape determined by the forces acting on it, which in the case of the Earth's oceans is mostly gravity.

The centrifugal force from rotating once per day is not that big, even if the resulting lateral velocity is high.

It's tidally locked. If it was stationary, we would see a different side of the moon once a month.

It isn't, light being cooler than shade is impossible.

Everyone should question what they're taught, and science encourages this, but some people end up going down confused paths and come back asking really dumb questions like "why is moonlight cooler than shade?"

It sure would be interesting to see if anything in the scriptures suggests an experiment that can be performed in a laboratory, but it would probably just look like fedora-tipping atheists flogging a dead horse.