Why did Palps announce his return rather than using the element of surprise?
Palpatine has been long-established throughout the entire saga as someone who strikes fear into his enemies. Seriously, he created the Death Star to strike fear into the galaxy to prevent them from rebelling.
Why would Hux betray everything he believes in just because he dislikes a coworker?
Hux does not betray the First Order altogether, he sent in the information so Kylo Ren would lose. Unless you’re referring to, “I don’t care if you guys win,” Hux is just saying that so Finn and Poe wouldn’t kill him.
Why does Palps tell Kylo explicitly to kill Rey, when his whole plan depended on Rey magically finding her way to Exegol un-killed?
Palpatine did want Rey to come to Exegol, but her parents abandoned her and now he doesn’t know where she is, so he turns to Ben Solo because he does know where he is, and turns him to the dark side — he wants the blood descendant of the Skywalkers to perform the Sith ritual so he would possess his body. Palpatine tells Kylo to kill Rey because at this point he no longer has any use for her and Kylo is already this far into the dark side, it is too late to possess Rey at this point.
When Kylo Ren redeems himself, this ruins Palpatine’s plan to have a healthy Force-sensitive person perform the ritual so he’d get out of the clone body he’s been suffering in for years — his line, “The Princess of Alderaan has disrupted my plans, but her foolish act will soon be in vain,” implies his plan was to possess Kylo Ren —, so he falls back to his original plan to have Rey perform the ritual.
EDIT: Removed swearing, as requested by JJB.