We don't know exactly how good or bad Kane and Olivia had it growing up. We've only heard bits and pieces. For the most part they seem to have grown up poor but mostly happy and relieved that they didn't have it as bad as so many others. When Olivia tells Elena that she wants to make the world a better place she says, "It's so brutal out there right now."B) How so? Until he was put in jail and entered into the gambit, his only complaint seemed to be that Callista was a pain in the ass when it came to teaching and that he didnt know who his father was.
But getting sent to prison for a crime you didn't commit soon after your mother supposedly dies? And then the Joy Facility has been absolutely hellish on the sub route - constantly being abused and paraded around like a loser. Of course it's not nearly as bad on the dom route, but he's still been a slave while the woman he thinks is his sister is treated like royalty.
Alexander placed some sort of bomb inside of him. Alexander is the reason that Kane was denied his birthright as a DeKock and a childhood with his father and his sister. Alexander is the reason that Callista has had to spoon-feed him lies his whole life, and fake her own death while he rots in prison.
Kane just doesn't know Alexander is the reason for all of this yet.
Of course he has heard of Alexander Karlsson... He and Olivia has spoken about him in the flashback, and Kane said "Oh that guy. He seems to have the most greedy and evil man alive title locked up. But I still bet it would be nice to be in his shoes...a life of luxury."Hell, up until the gambit, I doubt Kane even heard of Alexander unless there was some news on something he did.
I mean, the whole point of her faking her death was because the bomb was already inside of Kane... So your idea of it being placed in Kane after he was arrested is not even possible.c) As far as we know, in accordance with the story, Alexander caught her trying to escape but wound up letting her go in exchange for her following his demands. I doubt she came back once she left.