If Kane started k5, then he forgets the bracelet in the previous room, and that's it. Don't think Kwame can blackmail Kane about anything, no one can even activate the bracelet besides him, and Kane has done nothing wrong anyways. If he starts k6, then he sees the bracelet's message. No point in keeping it past then anyways. Maybe Kane just throws it into the trash bin where it belongs at that point? If Dominique quickly promotes him to k7 then maybe he forgets the bracelet back then too, but I can't remember.
When was Alexander Karlsson opposed to Callista having a child? I haven't re-read the earlier episodes in a while... Are you talking about that flashback with Luke? We don't know the story behind that yet, but I think we can safely say that Alexander very much wanted Callista to have a child... so long as it's his child.
Kane picks up a few times when someone says 'is' not 'was'. But really, if your mother died years ago, you wouldn't expect her to be alive just because someone says she's a genius. The bit where Elena told him that his parents were together in the room, and that his dad and Alexander had a falling out -- and then Kane asking Olivia if his father was Alexander the next scene after has been pointed out already. Whether that was poorly done, or Kane being so shocked that he had a bit of a brain fart is up for debate I suppose.
The characters aren't as one dimensional as you're making them out to be. Like, Olivia isn't just an 'acting genius'... she's supposed to be brilliant all across the board (though this brilliance mostly happens off screen). I would say Kane is likely the same way. But his specialty is supposed to be his 'gut instinct' at least according to Olivia. His ability to make good quick decisions.
I'm not sure what you're saying at the end there about the Gambit, but there seems to be a lot of confusion about the Gambit anyways so I'll explain what the Gambit even is (at least from what we know).
Kane and Olivia's tests are different... they're being tested for different things.
If the Gambit is successful, then what's supposed to happen is:
-> Veronica is to give up control of the company to the son of Kane and his worthy daughter, but she (Veronica) will retain full authority over all the scientific aspects of the company. Because of this, and the fact that she's running the Gambit, obviously leaves her ineligible to win the Gambit.
-> Until the child is capable of running the company himself, either the mother, or Kane, or both of them will run it. (Depending on if Kane is worthy or not)
-> Apparently there's still some stuff hidden behind 'doors' whatever that means. We don't know this bit yet.
(But I don't have much faith in the latter, too many things point to it being Tess).
