^ I'll call him "old Toudou" to distinguish from "new Toudou" = boss lady
Why do I get an image of Saburota helpfully offering his glasses frames and Yukio punching him in the face. (Given how Yukio already strolled in and was like "Lucifer, you're full of shit", I am near 100% sure that the next time Yukio runs into Saburota, things will get violent fast.)
Because I still stick on
my interpretation of the Toudou-Yukio relationship, I don't expect to see much interesting interaction in the future. Moreover, now it seems like old Toudou's words about Yukio were not too wrong, so I don't see why Yukio has to be angry. I think their remaining problem is that old Toudou once tried to kill Yukio, so Yukio might find some way to revenge for it.
^ The demon kings except for Samael. Mephisto knows what's going on and gives zero fucks. Probably because Satan is happy with him right now, since Samael is appearing to hold up his end of the bargain in training Rin so Rin's body can handle the flames. I wonder when Mephisto will break that agreement, because I'm pretty sure that he wants Rin as his own weapon to destroy Lucifer and Satan.
Mephiso doesn't have to do anything. What Satan gets is nothing more than a fake promise. Even after Rin's body becomes strong enough to endure the flame, who knows when will Satan has the chance to possess Rin?
(Maybe after 20 years when Rin also has a son and he is yelled by his son.) Mephisto clearly has advantage in this deal.
(I don't think we are sure Mephisto intends to "destroy" Satan for it seems impossible to do that. He only need to prevent Satan from get a body. And I do believe there might be some mechanism that all demon kings can't directly disobey Satan)
Wait, does Satan say "That's an interesting woman..." after Shiemi gets kicked? If true, that foreshadowing makes me very uncomfortable... 
Rather than after getting kicked, it's more after she told Yukio not to leave.
To me it sounded like a father-son conversation where the father is like "nice girl for you" (not for himself) and the son is like "don't get involved".
Though I like this headcanon, to me Satan's comment sounds more like "How amusing(
面白い) this weak girl thinks she can stop me"
My own headcanon is that Satan prefers mature woman.
In fact he has just broken Komaken without knowing what would happen to Rin. He doesn't know even if his brother could die bc of this, and instead of being worried he just joins the bad crew.
Satan broke Koumaken, not Yukio.
And he still doesn't mind if this kills Rin, he just takes off before knowing if he's okey.
He just shot his brother. It’s more like he expects him to recover.
Well he says : "I don't know what will happen when I go to the Illuminati. I might die too. In the unlikely event that (literally "a probability of one against ten thousand") we both survive, I will definitely become stronger than you."
So he knows Rin might die. If not from the broken sword, maybe from the order.
But Rin is surrounded by friends, leaving or staying might not make much of a difference in his chance of survival.
And he cares whether Rin survives or not. If he dies, who will he show off his strength to?
Oy vey. I could rationalize Yukio's "just die" from chapter 2 as an an expression of grief, since he kinda lost both his dad and his "human" brother in one night. But between this "yeah, you might die, I might as well, but that's a sacrifice I'm willing to make" and how Yukio has no visible reaction to Satan gleefully announces his plan to take Rin's body, I think it's safe to say that Yukio is completely disconnected from Rin. He doesn't feel a thing right now towards Rin, not love, not even anger. His regard for Rin is nothing but twisted shallow admiration.
But... I think this is how he really has felt for some time. And it explains a lot. His reactions to Rin have never struck me as someone close, but as someone estranged reacting to shadows.
Yes, the problem is not he wants Rin die or he doesn't save Rin, but it's that Yukio's reaction this chapter kind of an ultimate prove that Yukio doesn't feel Rin as a family member, but more like a competitor in a competition.
Although we shouldn't surprise since Yukio already shoot Rin last chapter and the hint was already there in chapter 2. Or it was also in the funeral scene in chapter 1 when Yukio just walked away. So far, Yukio's protection on Rin could only because he has promised Shiro.
Sadly, weather or not Rin & Yukio both survive, I think it's way to late for any kind of reconciliation now that we know Yukio only really cares about power and knowledge for himself, that and being better than Rin. Katou wouldn't be able to do it without looking like she's pulling it out of thin air.
I still believe there will be reconciliation, kind of. Like said many times before, it'll be rough before that happens.
Yeah, this is gonna be tough to repair but not impossible. Yukio's demeanor on the helicopter isn't that of someone comfortable with what they've done. More like someone rationalizing.
It depends on what a "reconciliation" or "happy ending" means. I think we will have an ending that Yukio apologize to everyone and stay as a good person, but he and Rin won't live together and won't be so close as before.
Contrasts with the Order keeping Rin on a tight leash. It'd be interesting to see what he does with that freedom. I kinda wonder if his adversarial nature will lead him to clash with orders. Somewhat ironic if their blind encouragement of his darker side leads him to rebel against them.
It could be that The Illuminati has flat organization hierarchy and people can freely talk to Lucifer with their own preferred style (Shima was also very casual in chapter 56). It makes sense if people join Illuminati because they hate bureaucracy of the Order.
Anyway, I believe Lucifer and other Illuminati members are aware the possibility that Yukio will against them (even if they didn't, they should know after the end of this chapter).