there are several books including a "public book" that all exchanges publish and an "internal book" that each exchange has.
in case of the "internal book", it is always ahead of the "public book", as changes to it "published" after events occur internally and this "internal book" is updated.
this is important bit, as an individual exchange "knows better/earlier" than the "public".
Yes.
...submitting into a black box what some security is worth to them.
These are Dark Pools. https://en.wikipedia.org/wiki/Dark_liquidity
Are there any good papers/articles modeling different market set-ups?
These are often called Crossing Networks. https://en.wikipedia.org/wiki/Crossing_network