Is it permissible for the husband to take back his wife, who was divorced by mutual agreement (verbally), before receiving the divorce certificate, and then remarry her through a new civil contract, and is consummation considered a pillar for the validity of this marriage after the return?

Divorce takes effect simply by uttering the words and does not require documentation. A wife can be taken back immediately after her divorce and before the issuance of the divorce document, as long as she is within her waiting period (iddah). The taking back (revocation of divorce) occurs merely by an explicit verbal declaration such as "I take you back," "I have taken you back," "I restore you," or "I hold onto you," or by an implicit statement with the intention, such as "I held onto her" or "I took her back." For the validity of the marriage, consummation with the divorced wife after taking her back is not a condition. It is advisable to have witnesses to the taking back of the wife to avoid disagreement.