Has a divorce occurred in the aforementioned cases, especially with the husband's conflicting statements and the wife's denial of some of them?

Swearing by divorce is reprehensible due to the risk it poses to marital life, as it leads to the pronouncement of divorce upon breaking the oath, according to the majority opinion. Your brother has done this and has broken all three oaths. Therefore, his wife is unlawful for him until she marries another husband, based on the Almighty’s saying: "And if he has divorced her [for the third time], then she is not lawful to him afterward until she marries another husband." This is according to the opinion of the majority of jurists. However, according to Sheikh Al-Islam Ibn Taymiyyah, he is only required to offer an expiation for breaking an oath. It is advisable to refer to the competent religious authorities regarding matters of divorce.