Good questions. Obviously, I do not have anything like close to having full knowledge of when God has intervened in history. I will say this: the normal situation is that God gives us free will and normally he does NOT intervene in history. He allows us humans free reign over our own lives, and only intervenes for a definite purpose. It is my belief (but only my personal belief) that God only intervenes when it is somehow related to his plan to provide for forgiveness of sins. Therefore, the only examples I can list are of this sort.
1. He intervened when he sent the flood to judge, but also to create new beginning for Noah and his family.
2. He intervened when he brought disunity to the city of Babel so that people would not destroy themselves.
3. He intervened to free Israel from Egypt and to give them the Promised Land.
4. He intervened to send both Israel and, later, Judah into captivity using Assyria and Babylon, and later to bring Judah back from captivity, using Persia.
5. He intervened in the time of Christ, both so that he would be crucified and raised from the dead.
No, the story of the witch at Endor does NOT prove the existence of ghosts. What it DOES “prove” is that there is life after death. Samuel was not a ghost. A ghost, by definition, is a spirit who lurks around in this world, still having some sort of presence here (not that I believe in ghosts, or disbelieve for that matter, just to define the term). By this definition, Samuel was called from Hades, and was not a ghost. He spoke from the realm of the dead, and was not a spirit, lurking in our world.
Schrodinger’s cat is a philosophical illustration. Schrodinger purposefully used an outrageous example to make his concept memorable. He did not propose that cats are partially dead and partially, as cats are not well defined by a wave function. Things which have a significant amount of wave-like properties measurably obey the uncertainty principle. In principle, cats do as well, but, as Schrodinger would point out, in practice, cats are not measurably of a wave-like nature, so the uncertainty of their being alive or dead is not a real thing. It is a concept, but not a measurable reality.
Nevertheless, Schrodinger, Pauli and Heisenberg proposed the idea of uncertainty for wave-like particles and for particle-like waves, and this theory has been supported by data matching the theory, so, for things like electrons and photons, Schrodinger’s Cat seems to illustrate reality. No, something cannot be both a linear combination of alive and dead. But the states of electrons appear to have that property.
This has absolutely no implication, either for or against, on the reality of soul or spirit. Besides, a person who is “dead” physically, still has a soul and a spirit, so, to be honest, your question is a bit of a non-sequitur. But still, it is a good question! ??