My theory is that Quote and Curly had a different creator from the other robots, and that this different creator had different intentions from the creator(s) of the killer robots. He therefore sent the two to destroy the Demon Crown. Kindof a no-brainer if you ask me. As for how he lost his memories... The closest thing I can come to a theory on that is that he got hit by Miakid so hard that he had to repair himself over a slow process that takes somewhere around ten years. A drawback to it though, being that if he runs this protocol, he's at great risk of losing his memories. The greater the damage, the more memories lost. And maybe Curly wasn't hit by Miakid quite as hard as Quote was, and woke up before he did, and that's how she remembered her name? There isn't really any evidence to support that theory, but it's the best I can come up with.