What are the implications of the condition being met for the first time, to which the divorce oath "that I will not hit her seriously for the rest of my life" was suspended, and is it permissible to take the wife back at the same moment, and how would she be taken back?

If you tie your wife's divorce to hitting her with serious intent, and you hit her, then the divorce occurs according to the majority of scholars. If it was the first or second divorce, you may take her back before her waiting period ends, either by an explicit statement or by action, according to some scholars. We advise against oaths of divorce and oppressing the wife by hitting her in ways not permitted by Islamic law.