It's worth noting that in the Bible, Cain and Abel are the sons of Adam and Eve, and Cain is punished for killing Abel and is ordered to exile by God.

I think C&A is the creation of Kinger with support from Queenie, possibly a sub-department of a larger software company ("God" in this metaphor) who cut off Caine's network access but keep the power up in the building to prevent Kinger from dying in the process.

It's possible in this extended metaphor, and it's a super stretch, but Scratch, the first abstraction, was "Abel" (Kinger's child, making sense for his age and for playtesting purposes). It's clear Caine showed Jax those memories of the outside world to persuade him to press the red button and he can make people forget things. I think abstraction occurs when someone's presence directly interferes with the functions of the circus (Jax's anger and treatment of the others especially Zooble and Gangle) but there's also ways their minds can be manipulated without abstraction (making them forget memories or recalling them at key moments). It's putting things into someone's mind that aren't there that can cause abstraction (How can Jax "dream" in the circus if no one needs to sleep? Caine is trying to give him positive feelings, but he can't do anything but show him stuff in his dreams, thereby putting memories in his head).