The only reason Rak wanted to fight Baam was because of the Black March. So why was he still following him around and calling him his prey if the reason for hunting him was gone?
He didn't want to fight the current holder of Black March. He wanted to fight Baam because within the tower, wielders of 13 series weapons are universally agreed to be total badasses. Baam was holding Black March, hence he must be a badass, hence he must be worthy prey. Black March was taken away - but Baam is still a badass. As of season 2, with him being the most powerful on the 20th floor by a wide margin, Rak's assessment of him is totally accurate.
Rak states himself that the black March is what makes Baam a worthy foe. He didn't even know what the Black March was, only that it was apparently extremely powerful. Baam even taunted him with this, throwing away his weapon and tellin Rak to "hunt him," which he was pretty pissed about.
There are multiple ways to interpret this. One is that Rak's opinion changed over time. Another is that he felt Baam tossing aside Black March showed an attitude unworthy of proper prey.
Fire-Forged Friends is a trope for a reason. The whole prey deal was shown after the Maze test to be little more than Rak being a bit Tsundere about it.
FUG and Baam
I really don't understand the way FUG is going about manipulating Baam. They need him to kill Zahard, who is more powerful than any of them by a huge margin (possibly excepting Phantaminum and Enryu - but their ranking is done by an outside agency, who don't necessarily have accurate reads of their full power, so arguably not even those 2 are assured of victory). I get that. And they plan to do this.... by essentially kidnapping people he cares about and using them as leverage. I get that too, it's really not a bad blackmail plan normally, but what exactly are they planning on doing if he actually SUCCEEDS in killing Zahard? BY DESIGN, their plan requires Baam to be more powerful than the guy powerful enough to kill every one of them on his own. The problem with any blackmail scheme is that eventually the person being blackmailed has had enough - sooner or later Baam is going to snap and decide he's just had it with FUG. So now they have created at a minimum the 3rd most powerful person in existence.... and he's pissed at them. And this looks like a good plan WHY?
Baam doesn't necessarily have to be stronger than them; it's just that as an Irregular, only he can kill Zahard. Others can help him or weaken Zahard. Likewise, when Mazino showed up, he talked about how a few hundred Rankers would be a "fair" match. It's almost certain an organization as powerful as FUG would have some sort of backup plan to make sure Baam doesn't defy the wishes of the organization.
That can be easily discounted by the fact that FUG hasn't already overthrown Zahard. If they were strong enough to take Zahard on, they actually don't need to KILL him at all - all they have to do is overpower him and then permanently imprison him somewhere and keep watch on him. They need Baam because they are no match for Zahard even WITHOUT his immortality, and they know it.
They are a really good reason that kill Zahard is better and simpler than just overthrown him. Assassinate logistic is much smaller than overtake all the 10 family (and guardians since they are binded to Zahard). Because they won't accept Zahard kidnapping or overthrown. And fight will be really more tough. On the other hand, murder Zahard need just one powerful attack one time. And the capacity to kill Zahard. It's Truth in Television, assassinate is a easy way to take a crown.
The problem is they train Baam/Viole to become a god. They do anything possible to make him over powerful, more stronger than them. They clearly want Baam become their god-like slayer. And Baam is a genius, he will certainly exceeds that. How can they hope to control him when he will be ranker?
Alternatively, they were a lot of possibility to manipulate him. They had choices of plan, the opportunity and the means to control it. But what? Yu Han Sung just tell the true to Baam and pissed him off. Okay. It's just sound stupid if Yu Han Sung works really for FUG. This blackmail gambit is really bad, because Yu Han Sung reveals it and because it includes a lot of hole.
Alternatively; they wouldn't care. Slayers to FUG are absolute gods, and to have Baam fulfill their prophecy and allow Mirchea to achieve his own power grab, they might not even care at that point that Baam would take his friends back or even give them back as a reward.
The point is that Baam would not just 'take his friends back.' If he's pissed enough to do that, he's probably going to be pissed enough to kill everybody in FUG for manipulating him down a course of action he never wanted to begin with.
Baam himself addresses this in a recent storyline, threatening to kill Xia Xia if she tries to manipulate his friends again. It seems that if Baam truly becomes a monster, FUG won't be able to stop him.
Word of God has stated explicitly that while Baam is powerful, he's not outrageously powerful compared to some of the other people in the tower, and that FUG's reason for wanting him is solely because only an Irregular can kill Zahard, not because of his strength.
Word of God don't address the issue. FUG clearly want and work to make Baam outrageously powerful. And pissed him off. Together, both of these actions can only conclude to a Epic Fail.
Even being really powerful doesn't mean you can protect your friends from a terrorist organization 24H/24, so Baam should remains quiet if he value their life after he defeat Zahard. Even if that isn't the case, their only goal is to kill Zahard, they don't seem to care about what will happen after this.
Even if Baam becomes far more powerful than anyone else, that doesn't mean he has the political clout or skill to be in charge. Killing Zahard would still destabilize the power structure in the tower. Opportunists in FUG would figure they can take advantage of that and avoid getting killed by Baam later (especially since he doesn't know many people in FUG). Revenge-focused FUG members might not care if they get killed as long as they have revenge. And of course there's the fact that Baam doesn't seem the type to kill others normally, so FUG might be safe from death even if they force him to kill Zahard. They just have to ensure they can threaten his friends which is so far easy enough no matter how powerful Baam might get.
Team Leesoo and Rachel
Did team Leesoo just forget about Rachel when Koon "died?" She's their entire reason for climbing the Tower, and they completely forget about it? I know they're preoccupied with Viole and all, but really? Was she not important enough? Even if Leesoo did know about Rachel's betrayal, did he never think to consider a connection between her and Koon's death? Or at least think "hey, I wonder what happened to that Rachel chick we were supposed to be helping climb the tower?
They know she is a traitor, so if they meet again, I suppose she will need something to protect herself, but I don't see what make you think that they forget about her.
Leesoo knows she's a traitor. He never told anybody else on the team, because it would destroy the team and eliminate their reason for climbing. While it would make sense if he told them about her after Koon's death, there's nothing to suggest that he did. No matter how preoccupied they were with revenge against Viole, it's baffling that they never once thought about her.
Just because it wasn't show on-panel doesn't mean it wasn't discussed at some point. Her attempted killing of Koon was VERY recent, chapter-wise. In the months since Koon's 'death', I'm sure they've talked about hundreds of things. If the author wants us to know, I'm sure it's going to come with some kind of flashback when one of Team Leesoo comes face to face with Rachel.