Is marriage valid with only the recitation of Surah Al-Fatihah and public announcement, but without a guardian (wali)? And does the divorce of an extremely angry and agitated man count?

First: "Al-Fatiha marriage" is invalid because it is a devilish innovation that lacks a guardian (wali) and witnesses. You both must separate immediately and repent to Allah. Then, the man can marry her lawfully through her guardian. As for the children, they are attributed to the man if the couple believed the invalid marriage to be valid.

Second: A man's divorce does not take effect if he reached a state of anger where he lost his sanity and his mind was blocked.