Is your wife considered to have been divorced after you said to her, "You are divorced," following an argument about her communicating with a foreign man, and then her mother called you to plead with you, and you said to her, " الخير إن شاء الله (It will be good, God willing)"? And how can she be taken back?

The words you mentioned do not constitute a revocation (raj'ah). If this divorce is not the third and final one, you can revoke the divorce of your wife before her waiting period ('iddah) ends by saying: "I have taken you back." It is more prudent to have two witnesses. According to some scholars, revocation occurs simply by engaging in intercourse. She must fear Allah, recognize her husband's rights, and safeguard herself for him. You, in turn, must fulfill your duty of guardianship by preventing her from engaging in forbidden acts and closing the doors to temptations.