Does the plaintiff count as divorced three times after her husband uttered the word of divorce repeatedly, especially the last time, which came in response to her saying, "If only I had known you were of lowly origin," even though she did not intend to accuse him of that? And is it permissible for him to take her back?

The wording of the divorce mentioned is an immediate declaration, not a conditional one. However, if the husband divorced you believing that you insulted him with "qaleel al-asl" (of ignoble origin), while in reality you did not, then the preponderant opinion is that the divorce does not take place. This is because if a divorce is based on a reason, and then that reason is proven to be nonexistent, the divorce does not occur. It is advised to present this matter to trustworthy scholars.