It's not possible to label a photon, but not all photons are indistinguishable. So can we rephrase the question as, are the photon properties, such as spin, conserved? If the photon that enters is entangled with another, is the photon that emerges also entangled?

The letter 'h' doesn't have an h sound in it (at least in American accents), and the letter 'q' doesn't have a q sound in it. (It's kyoo, not quoo.)

Marbles are not a good model of any particle at the quantum scale. But ethereal particles passing through each other freely is also incorrect. It's somewhere in between. It's somewhat comparable to electron orbitals, where you can fit a certain number into the same level, although the way they draw electron orbitals in high school textbooks isn't really accurate either.

Protons or neutrons with all the same quantum numbers except for opposite spin can freely occupy the same space. Even with different quantum numbers, they can pass through each other, although particles with different quantum numbers have different shapes of probability distributions, which means they're more likely than not to be found in different positions. Once all the quantum numbers in an energy level are used up, addition protons or neutrons must go in a higher energy level. While a particle in a higher energy level is more likely to be found further from the center of a nucleus, there is always the possibility it will be found near the center, in the same place a lower energy particle might be.