Is a man's saying to his wife: "By Allah, I will divorce you if you speak with her" considered a promise of divorce or a conditional divorce? And does the divorce take effect if the wife speaks with that woman about a different matter than what was intended at the time of the oath?

If a man says to his wife: "By Allah, I will divorce you if you speak with her," this is a promise of divorce and not a suspended divorce. Therefore, no divorce takes place if the wife speaks with the woman in question. However, if the wife speaks with the woman and he does not divorce her, the husband must offer expiation for breaking an oath (kaffarat yameen). If his intention with the oath was to prevent his wife from speaking with the woman about a specific matter, then the oath is particular to that matter, and he does not break his oath if his wife speaks with the woman about another subject.