I find before starting such discussions it helps to ask why your expect a given outcome first before declaring that outcome disproves a given theory.

Why would you expect gravity to be constant across the planet if it is an oblate spheroid with non-uniform density and varying composition instead of a homogeneous sphere?

Weight and mass are not synonymous, and electromagnetism is orders of magnitude more powerful than gravity. Under what conditions is the test for a levitating capacitor performed?

You are correct, heat does affect magnetism. However, the Earth's core is a large mass under extreme pressure, and it does rotate every 24 hours while interacting with the electromagnetic field of the sun. I don't know whether that affects these calculations of demagnetizing or not. I would hesitate to call this disproof.

If a guy did an experiment in the past, we can replicate it today, right? What if Einstein's criticisms were correct? How can we account for it and ensure that criticism is invalid while replicating the test?

Tesla is reported to have performed amazing feats, and while I doubt he was a charlatan, many other potential considerations must be weighed. Wireless transmission of power has been performed, but between interference with radio communications and the problem of the inverse square law over distance there may be good reason not to replicate them.

Light is strange. I don't claim to understand the intricacies of how light interacts with objects. I know there are reports of slowing light. I know there are reports that the alleged FTL information transfer have been challenged as in fact a miscalculation. I don't have the knowledge base to confirm or disprove anything there. However, I am willing to co conditionally accept the status quo of physics for now.

The real test is whether a given model more accurately predicts the outcome of experiments consistently over time. As an extreme example, flat earth theory fails to predict or explain anything, while the heliocentric spheroid earth model does predict and explain eclipses, retrograde planetary motion, the day/night cycle, the horizon, etc. and the flat earth criticisms I have seen can all be tested and rendered moot by checking the assumptions and testing in the real world.

Now, I am not saying your position is that level of error, but I am trying to find a standard for investigation of your claims.