Is it valid for the husband to take back his wife after he had issued a "final and irrevocable" divorce, attested to by two men, given that she had requested divorce multiple times?

If the first divorce was a single pronouncement, then this second divorce also counts as a single pronouncement, even if he says in it, "there is no returning," or "irrevocable," or "by three pronouncements with one utterance." In this case, the total would be two pronouncements, and he may take her back as long as she is within her waiting period (iddah), and one pronouncement remains for her. However, if the previous divorce was two pronouncements, then this third divorce takes effect and ends the marriage, and he may not take her back.