Well, using my limited knowledge, "cleaving" means to chop, break in half, split, etc. Twain means twice. So, perhaps it's like "you've broke my heart in half", something along those lines? hopefully this helps you.
Answer:
I'm pretty sure they're kinda like going against an opposite opinion about something, and you're adding your research and evidence for why your opinion or topic you're arguing about is better than the other's.
Answer:condutor
Explanation: a conductor is anything to allow electricity to pass through it.