1) If we have a photon that produces a pair of electron and positron, the electron and the positron is spin entangled after the production. The total spin of the produced pair of particles are the same as the spin of the photon due to spin-conservation.

2) Likewise, if we have a spin-entangled electron and positron with a particular total spin, and is annihilated, it will produce a photon of the same spin.

3) If we have non-entangled electron and positron, then a photon will be produced with a spin of statistical probability depending on the spin of electron and positron before annihilation.

Is any, or all of them wrong?

Also, how are entanglement interpreted in the community of physics? For example, if we have an entangled electron-positron pair, is there some sort of interaction intermediate linking the electron and the positron when one of them is measured for z-projection of the spin so that it automatically determines the z-projection of the spin of the other particle? Or do they have rather agnostic view of how the two particles are entangled ("don't know how but it does" attitude)?