1) So FUG needs an Irregular to kill Jahad, because when Jahad became king of the tower he made a contract with the guardians that doesn't allow regulars and rankers to kill him. Basically all the heads of the were given immortality by a guardian during they're climb since they were there first people to ever enter the tower. However 1, the head of the Hendo family was cursed, as the guardian didn't want to give him immortality, unless he decided that all his descendants and their children would have shortened lifespans, which he agreed to.
Baam as in irregular is not bound by the rules of the tower, remember. So he can kill Jahad. That's why FUG wanted to use him or during the workshop battle melt him into the thorn so they could have a weapon with the power of an irregular.
Now remember there are only 5 irregulars in the tower, Baam, Rachel, Enryuu, Urek, and Phantanium. Phantanium being the strongest being in the tower. He's not active, but when he first came into the tower and reached the 134th floor that Jahad rules, he killed a bunch of the Jahad rankers and destroyed the castle before leaving. Rumor is Headon's been searching for Enryuu but can't find him. Rachel wasn't chosen by the tower, but fell in as Baam pushed the doors open, so she doesn't have any special gifts and is weak.
Fug wants Baam at first, just due to his irregular status, but realize he is super gifted. Plus most of the higher ups believe he died on the floor of tests, so they're not aware of an irregular roaming the tower giving FUG the element of surprise with Baam.
2) We don't know much about Wangnan other than that Hwa Ryun called him the worst mistake of the 10 families and that he carries a Jahad ring. The only other character we've seen with such a ring is Karaka. Theories right now is that one of them could be the Prince of Jahad, but nothing is for sure. We also know Baam's cave that he was locked in had the Jahad symbol making it possible he has some connection to Jahad as well.
3) The floor guardians require regulars to make contracts with them in order to use Shinsoo. The ones who don't are members of the 10 families, because they're grandfathered in by the contracts their family heads made and irregulars. The floor of test guardian mentions that Baam making a contract with him is like shackles, we don't know why, but if the crown game is any hint, the shinsoo seems to move to protect Baam on it's own if there's not contract. The guardians are the rulers of the shinsoo on the floor, which is why they require the contract. It's just a system that was in place before anyone even entered the tower. The guardians were thought to be the gods of the tower until Enryuu killed one on the 43rd floor. The guardians can make other contracts outside of just Shinsoo use, which is how the family heads got immortality by making additional contracts and Jahad made a special contract so that no one in the tower is allowed to kill him, except as mention irregulars, who do not have to abide by the rules, because the tower itself chose them, not Headon.
4) Karaka is one of FUG's full fledge slayers, so he is considered a God within the organization. He was also mentioned by Ha Jinsung, Baam and Karaka's teacher, and one of the top 100 people in the tower that Karaka is climbing the ranks quickly. This coupled with a splinter within FUG siding with him, he has a lot of power in FUG. There are 11 slayer positions in total, 5 of the slayers are "missing", the 2 active slayers are Karaka and the founder of FUG Grace Mirchia Luslec, and then 4 open spots. We now know White is one of the missing slayers, as is Yama who has sided with Karaka. So while Luslec wants Baam alive and is the most powerful person in FUG, Karaka in theory would be the one of the more powerful people in FUG.
5) Urek has taken an interest in Baam and Baam has taken an interest in Baam, so it would make sense for Urek to come back, especially once they get to the 77th floor, which is the floor Urek owns. He got the floor by passing Arie Hon's special test. It is where he headquarters Wolhaiksong. He also will probably be pretty instrumental in the story either from the 77th floor up or after Baam becomes a ranker, as Urek is the only active irregular in the tower besides Baam and Rachel. Plus Urek is friends with Yuri, so we may see him sooner if she sticks around. Either way he has a role to play.
6) Kaiser may have a contract with the guardian and is being forced to stay on the floor by the 10 families, since they use that floor to dispose of threats and people they dislike. Otherwise Lero-ro, the guy who looks like Pikachu, said that once people in the tower learn to control Shinsoo, it slows their aging and can allow them to gain eternal youth, control over the elements, immortality,etc. it's basically limitless, which is how everyone in the tower is so old, for example Anak and Androssi are both estimated to be around 300 and Yuri being 500. It is also why Urek climbing the tower in only 50 year is considered extremely fast. Shinsoo can even be used for food supremely talented Shinsoo users like Enryuu are said to be able to create life using Shinsoo. So those climbing the tower are able to live so long due to Shinsoo, except for those in the Hendo family, who only live 100 or so years the remaining life span is transferred to the family head, due to his immortality contract with the guardian of the 100th floor.
