Questions arising from the experiment of Greenberger, Horne, and Zeilinger:

The upshot of this article is that the x and y components of the spins of the three particles cannot be in possession of unmeasured values. Once again we are forced to reject the assumption that observables have values irrespective of measurements, inasmuch as this assumption is inconsistent with the quantum-mechanical assignments of probability.

Caustic Sunset (detail) by Eric J. Heller.

The outcomes of the measurements discussed in this article are strictly correlated: Whenever only x components are measured, the product of the outcomes equals –1, and whenever one x component and two y components are measured, the product of the outcomes equals +1. Any two outcomes suffice to predict the third outcome.

I can tell you the situation in respect of the last question straight off. Nobody has the slightest idea how these measurement outcomes come to be correlated. Nobody even knows how these measurement outcomes can be correlated. In other words, you understand this as much as anybody else!

Einstein, as is widely known, wasn't happy with quantum mechanics:

I cannot seriously believe in it because it cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance.

Einstein did not know Bell's theorem. We know now that

there must be a mechanism whereby the setting of one measurement device can influence the reading of another instrument, however remote (John Bell).

Spooky actions at a distance are here to stay.

Question arising from the bomb testing experiment of Elitzur and Vaidman:

If D₂ clicks, we learn that (i) the bomb was present, and (ii) that the photon never came near the bomb.