Is what was said in the aforementioned situation considered an ambiguous divorce (طلاق كناية) or not? Is the ignorant person excused in the case of an ambiguous divorce? And what is the ruling on obsessive doubts (وسوسة) in such cases?

What you mentioned, such as your saying to your wife: "Stay with your family, I don't need you," or what you sent her via mobile phone, that she is "divorced," is considered a kinayah (allusion) of divorce, by which divorce occurs if you intended to effect it.

As for your saying to your wife: "You are divorced once," this definitely effects divorce, because it is an explicit (sarih) pronouncement.

Regarding your anger, if it was severe to the point of making you lose awareness and discernment, then divorce does not occur in that case.