Does a photon's spin wavefunction collapse when detected by a photon detector? Assume two entangled photons A and B have the same spin but travel in different directions. When Photon A is detected by photon detector (e.g. photomultiplier) on its path, does Photon B's spin wave function simultaneously collapse?
 A: There is no collapse in standard quantum mechanics. (By "standard," I mean the parts of quantum mechanics that everybody agrees on and that are needed in order to get anything done: stuff like complex amplitudes, and observables as self-adjoint operators.) Collapse is a feature of the Copenhagen interpretation. It isn't an actual physical process that we can observe.
I think you're describing an entangled wavefunction of the form
$$ c|\uparrow\uparrow\rangle + c'|\downarrow\downarrow\rangle ,$$
where we have $|c|=|c'|$. Suppose we let Y mean that the detector sees photon A as having been spin up, N if not. Then after detection, the wavefunction of the photon has been entangled with the wavefunction of the detector, like this:
$$ c|\text{Y}\uparrow\uparrow\rangle + c'|\text{N}\downarrow\downarrow\rangle .$$
Nothing has happened to photon B. All that has happened is that the entanglement has spread to include the detector. If you like the Copenhagen interpretation, then you can say that detection then collapses the wavefunction so that we have something like
$$ |\text{Y}\uparrow\uparrow\rangle.$$
Collapse applies to the whole universe at once. This is why the Copenhagen interpretation is sometimes referred to as the disappearing worlds interpretation. Whereas in standard quantum mechanics we would just say that we no longer care about the amplitude represented by $c'$, Copenhagen says that that entire universe abruptly vanishes.
If you add a second detector, which looks at photon B, then you can check what happens when the two detections are simultaneous in the lab frame (and therefore spacelike separated in all frames). An experiment of this type is Guerreiro et al., "Single-photon space-like antibunching," https://arxiv.org/abs/1204.1712 . (They don't use entangled spins, but it's conceptually the same.) The result is that the correlations are present regardless of the fact that the detection events are simultaneous. But this does not mean that Copenhagen-style collapse is an actual process.
