Help me understand and fill in any knowledge or information I've missed.

The Hive worship Oryx, and have an active hatred/war with the Traveler, demonstrated by stealing a shard and attempting to use it to hurt the Traveler. They appear to draw other worldy powers from this deity, similar to Guardians use of the Travelers light.

The Vex worship The Black Heart, understanding it's power and being unable to comprehend it, they determined worship was the best course of action.

The Cabal worship no one but expansion. They have no deity and draw no powers from higher beings. They are self sufficient in that the Cabal we have seen are likely a very small portion of their empire.

The Fallen also appear to worship no one. The fallen are in fact not unlike us, in that they were once great and powerful, and are now left to scavenge the galaxy with what little resources they have. Do we have any clues as to their origin and fall? It's not implausible that they were at one point protected by the traveler same as we are, except for in their case the Travel either willingly left or was forced out by the Darkness.

The Awoken follow their queen, and have a strategy seemingly based on survival. They don't like outsiders and don't venture out too much, considering many endeavors to be death. Given their past, this seems like a reasonable strategy and mindset for them.

Loyalties to each other.
Question: Has anyone ever seen the Hive fight the Vex? Those two appear to be our primary enemies, them having taken direct action, currently and historically, against the traveler. We know that both of them also showed up just before the Darkness came last time.

I see the Cabal as a race that could come or go. They have a pride in their power, but if a war of gods breaks out in our solar system I'm not sure they have a vested interest in picking a side. They might be convinced to choose one for their own well being, but we certainly see them outright attacking the Vex and vice-versa.

The Fallen seem like the most likely race to switch sides. I have a feeling their past has intersected with the Traveler and Darkness before, but that they have little knowledge of that or anger issues. It seems likely that if their history were explained to them, they might join us. They also have no love of the Hive, and also outright attack them and every other race on every single planet, correct? They are described as nomads and scavengers, but they certainly pick very harsh fights and enemies for scavengers. Seems like they could pick apart Earth for centuries before needing to engage the Hive on the moon.

tl;dr
The Hive follow a Darkness like god, draw power from said god, and attack the Traveler.
The Vex follow a Darkness like god and attack the Traveler.
The Cabal follow no god, and have not attacked the Traveler directly, but they do attack the Vex.
The Fallen follow no god, have not attacked the Traveler directly, but they attack every other race.

Thoughts?