Foucault Pendulums are damped oscillators that stop naturally, mainly due to air resistance, so they're given a periodic nudge to keep them going; no mystery there. The Foucault Pendulum was intended to demonstrate Earth's rotation (by its precession in response to the Coriolis effect), not to be powered by it. If that was possible, we'd see 'free energy' and 'perpetual motion' machines using them, or perpetual clocks (there are 'perpetual' clocks that run off atmospheric pressure changes).
The existence of the Allais effect is debatable, having conflicting experimental results - several high accuracy gravitometer studies have found no effect. It may be a systematic experimental error, although there have been various highly speculative suggestions as to how it could be explained if it's 'real'. None I've yet seen invoke a flat Earth.
But assuming, for the sake of argument, that the Allais effect is real, we should expect flat Earth theory to provide an explanation for it. Can you provide an explanation, or point us to those threads where you've "...
discussed the science in great detail." or the links to papers by qualified mathematicians, physicists, & engineers that provide a full mathematical treatment of flat Earth theory, that you say you've posted "
on numerous occasions on past threads"?
Or does the apparent absence of that information on this site suggest that the Round Earth Conspiracy has taken control of Christian Forums and deleted them?