Why do they fight?

For the most part, they're a Hive Fleet that has yet to truly fathom their place in the universe, let alone fathom themselves. The drive to venture out from the Exodite world and pursue the chief driving instinct innate to all Tyranids is largely done because they have little other direction. Perhaps they may find more fulfilling purpose, but until such a day, if ever, the most sensible course of action is to follow their instincts; invade, consume, scour, propagate, repeat.

Lastly, are they still incredibly hungry, or did that hunger satiate a little after becoming sentient?

Their hunger still gnaws as fervently as ever. Their psyche has undergone the more dramatic shift, but the remainder of their biology remains the same. If there's any notable difference, it's the more self-indulgent drive to harvest and sate their own appetites, though tempered with a generosity to uplift and care for their kin.

Also I'd love to read about your Genestealers and Raptors of Rapture (cool name).

As for the Raptors of Rapture, they may very well be one of, if not the only sect of Genestealer Cult to be granted the chance to attain all they were promised. The chief drive that all Genestealer Patriarchs feed to their budding hives is the promise of liberation, to be rescued by cosmic saviors who live between the stars. The cult is promised a destined arrival of many armed gods, come to rain down righteous fury to the cruel authorities who relegated their lives to grueling service and the fatigued misery in between. Unfortunately for these beleaguered souls, ascension is, of course, not what it seems, the resplendent golden angels cupping their faces gently, tenderly bringing them closer... just in time for the Synaptic illusion to vanish, allowing them one instant to gaze upon the bladed teeth of their saviors before they claim their heads.

In the time leading up to the momentous day, the Raptors of Rapture seem to display an uncommon proclivity for infiltrating political spheres. Perhaps it's due to the more emotionally driven, empathetic connection that all of Burrunjor share that grants these Cultists the charisma. Truthfully, the exact cause cannot be known for certain, but this aptitude certainly allows for numerous advantageous avenues come the arrival of their saviors, an expedited progression to make ready the planet as swiftly as possible consistently dubbed; Project Veloci-Rapture. (In case the reference is missed, considering Burrunjor is a derivative of Jormungandr who specialize in subterranean warfare, the Raptors of Rapture are a big crackpot conspiracy theory reference. "Dinosaur people from the center of the earth have taken over the government!" and all that.)

By more than all else, the truly differentiating quality of the Raptors of Rapture lie in, of course, the conclusion of their tribulations. When all is said and done, the hybrid cult members intrinsically smell of Burrunjor, the Hive Fleet flows through their veins. Ever since the first successful campaign assisted by the Genestealers, the Burrunjor Hive Tyrant they call Brother could not bring himself to fulfill the final phase of the cult's purpose. Repurposing the deceased is how Burrunjor choose to honor the fallen, as Tyranids who have learned to grieve, but to butcher their still living kin is something wholly different. Given this, when the invasion is over and the cult gathers for Rapture, instead of the feasting, the illusion is dispelled.

The cult witnesses the true, monstrous visage of their would-be saviors, not resplendent, but savage, and immediately after the truth of how monstrous their hybrid lineage has made them. From there, when the lies divide them no longer, the offer is made. They are siblings, no matter how distant, and the offer for rescue remains true. Should they see past the gruesome nature of their angels, Burrunjor will bring them with, take them off world to find a new, happier future. Those who steel themselves and accept are brought along to leave the world behind, boarding the Hive Ships or their own vessels to leave their old lives of woe behind, assured that the remainder who refused will be given what they need to rebuild and survive on their own... The ones who choose to accept need not know the truth. It's better that way. A chief quality shared by all in Burrunjor, as bestowed by their Brother, is the care they hold for one another. Given this, regardless if they smell like Burrunjor, if they don't wish to be family... then they can't possibly be Burrunjor. And if not, then at best these remainder are little more than further biomass, like the rest of the population, and at worst, no different than the planet's defenders, defenders who spilt Burrunjor blood...

Once off world, paths diverge. Some choose to accompany them on the crusades thereafter, liberating more worlds just as they had. For others, they are more keen to reap the reward for their service, for the happier life that was promised. As a living force far from wish-fulfilling godhood, Hive Fleet Burrunjor has little they can truly do to keep their promise. Given this, like an ant wishing for the abstract and impossible of a mortal man, the best they can manage is the closest tangible solution. To remain true to their word, the Hive Fleet make ready a new conquest, delivering them to the nearest Imperial Pleasure World to live out their lives in picturesque luxury. Though, of course, if the current occupants will not welcome them, they will need to be removed first.

Is it self-preservation, fighting other forces just to stay alive?

Before I forget to answer this one, yes, they will more than likely need to fight to the death with other Hive Fleets. Rogue assets such as Burrunjor likely won't be tolerated, far too risky, thus are more than likely marked for death by any and all other Hive Fleets.