Xayide wants to supplant the Childlike Empress through Bastian despite her status as a Fantastican? The beginning of the book defines all Fantasticans as respecting the Childlike Empress and never wishing to overthrow or harm her because she views them all as equally important, and never judges or commands them. Y'gramul the Many is a prime example of a foul creature who respects Auryn and the Empress because she respects him and his nature. Xayide goes against this previous characterization of native Fantasticans by wanting to supplant the Childlike Empress and rule through manipulating Bastian as a puppet emperor. She could be the same kind of being as the Gmork who have no world of their own and thus want to take over or destroy worlds like Fantastica, but there is no hint of it except that her actions vaguely imply it.
Xayide has no expectations of actually ruling through Bastion. She recognized the City of Old Emperors when she followed his trail there, meaning that she knew full well what would happen to him. She was just trying to drive him to his own destruction for the evulz. (Also, Ygramul is a she.)
It's also worth noting that Xayide shows up literally after Bastian has been sulking after a minor argument with Atreyu and Falkor and has deep-down wished to be seen as dangerous, powerful and someone who can't be pushed around. In a way, she's really just fulfilling that wish for him, whether she realises it or not; every action he takes and that she manipulates him into thereafter works towards making him come across as dangerous, powerful and someone who shouldn't be messed with. Similarly, it's probably no coincidence that she's destroyed almost immediately after Bastian has escaped the City of Old Emperors, renounced his previous wish and has instead wished just to find someone who will treat him as an equal part of a community; she's no longer needed.
The G'Mork is trying to help the Nothing consume all of Fantasia, so he can control humans once their imaginations are killed... except doesn't "all of Fantasia" include him?
Note this is only movie-only. In the book, G'Mork tells Atreyu that, he only appears as a Werewolf in Fantastica, but he is neither of Fantasica nor of Earth. Rather, he's one of many creatures who have no world to call home. As a result, he is able to traverse the worlds freely and assume any form that is native to the world he goes to. His rationale for helping the Nothing is out of his bitterness for not having a world to call home.
In the movie, it's implied that an unseen evil is responsible for the Nothing and has sent the G'mork to Fantasia to kill the meddlesome Atreyu, probably with a pact that he will have a place in the new order created in the human world from the resulting chaos. Having failed to complete his mission, he is found abandoned in the Spook City that will soon fall to the Nothing (assuming that wasn't to be his fate all along). note Deleted lines from the script have him resignedly tell Atreyu, whom he doesn't recognize like in the book, to leave him alone, and that he has grown weak from searching for his quarry for so long - the removal of that part of the dialogue also took any possible shred of sympathy for the G'mork, keeping only the vicious portrayal.
Some of his lines in the film suggest that he's been driven mad by the knowledge that he's a character in a storybook and his destiny is always to be killed by Atreyu at the end, meaning that none of his actions matter and his entire existence is pointless. One could speculate that the real reason he helps the Nothing is because he desperately wants to end his own suffering by erasing himself from existence.
Somehow I'd always gotten the impression that G'Mork himself was a manifestation of the Nothing. The Nothing turned into Something to do its bidding. Probably because of the scene where G'Mork just comes bursting out like he'd only been created that moment. It's still a huge thing that consumes whatever is in its path... but now it's a wolf.
G'Mork was tasked with killing Atreyu and very nearly succeed in the Swamps. And yet he doesn't recognize Atreyu at the end? Granted he wasn't covered in mud this time around, but still shouldn't he have known what Atreyu looked like?
He only saw Atreyu from behind in the Swamp. Also I think it was supposed to be implied (albeit not shown well) that it was night at the time. There was certainly a lot of mist hampering vision.
At this point Atreyu had lost Auryn, which is probably why G'Mork didn't recognize him.
If Atreyu hadn't found that sharp stone fragment, Gmork would have easily killed him in their confrontation. Lucky thing, too, because he was ordered not to bring his weapons on the journey because... uh, why was that, exactly?
In the book, the reason for the abandoning of weapons is because Atreyu carries Auryn. Whoever carries Auryn is to regard all Fantasticans the way the Childlike Empress does - all as equals. And all Fantasticans are to respect Auryn and not harm the bearer as though the bearer were the Childlike Empress herself. In the book it is never anticipated that a non-Fantastican outsider would be sent to kill Atreyu, although the Gmork gets permanently chained up and dies of exhaustion and hunger before he can complete his mission. Atreyu never needed or used a single weapon in the book. The stone knife in the film is there purely to satisfy the audience expectation that the hero should always personally vanquish the villain.