What is the ruling on a conditional divorce in the case where the husband swore to divorce if the wife resumed certain actions, then the wife resumed only one of them, and the husband beat her? And does divorce occur every time they quarrel?

The pronouncement of divorce is the husband's prerogative, and your husband's statement is considered valid as long as he informed you that he was truthful in his oath according to his intention. Therefore, turn away from the whispers of doubt and anxiety, seek Allah's help, and supplicate frequently.