What is the ruling on divorce in each instance mentioned in the question: does a divorce occur with three pronouncements or with a single one if the husband enters a chat, and does the oath take effect if the husband speaks to his wife or sister via Facebook after asking her to remove relatives?

The husband's saying "okay" after his wife asks him to swear an oath by divorce does not result in anything. Likewise, his recounting of a previous divorce that occurred does not constitute a divorce. As for his swearing by triple divorce not to enter the chat, the fatwa (legal ruling) we follow is that triple divorce occurs if the husband breaks his oath. The determining factor in what constitutes breaking the oath is the husband's intention and purpose. If he intended absolute abstinence, he breaks his oath by entering absolutely. If he intended to abstain only from conversing with foreign women, then he does not break his oath by entering for other purposes. The ruling depends on knowing the husband's exact wording and his intention. Therefore, the matter must be presented to a Sharia court or to trusted scholars.