Have any of Einstein’s equations or theories proven to be wrong?
Yes, all of them when applied to subatomic particles. Einstein's theory of relativity applies to very large objects like solar systems and objects traveling near the speed of light. In those cases his theories give accurate results when compared to the measurements. But when applied to subatomic particles his theories do not match the measured results. That is where quantum mechanics come in. Quantum mechanics describes subatomic particles accurately.
Einstein's theory of relative and quantum mechanics contradict each other. They can't both be true, and both are probably false. So the hunt is on for the Theory of Everything (T.O.E.) that will describe both objects moving near the speed of light and subatomic particles. One of the candidates is super string theory. This is strictly theoretical since the proposed strings are too small to detect with instruments. One of the things it predicts is the graviton, a particle of gravity. But the graviton has not shown up yet.
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cosmological constant
“God does not play dice.”
Yes.