What is the ruling if the husband takes back his divorced wife, who had requested the divorce and was divorced by him? Is her waiting period a revocable or an irrevocable divorce? And when can she obtain the divorce certificate?

The basic rule regarding divorce is that it is revocable, unless it completes the third divorce, or occurs before consummation, or is for a consideration (khul'), in which case it is irrevocable. If the husband takes you back after consummation and before the 'iddah (waiting period) ends, and the divorce did not complete the third one or was not for a consideration, then the return is valid, and your knowledge or consent is not required, though it is recommended to have witnesses for it. As for the divorce document, one should refer to the competent authorities regarding it.