Is she still his wife after the aforementioned events, or has the divorce already taken place, especially with her repeating the phrase "Divorce me," and his saying, "You are divorced with one pronouncement," while he was angry?

The wife must repent to Allah and stop asking for divorce, for it is a great sin and a corruption of families. A severe warning was mentioned in the hadith: "Any woman who asks her husband for divorce without legitimate cause, the scent of Paradise will be forbidden to her." As for the phrases mentioned, divorce does not occur by इशारा (gesture) or shaking the head, nor by promising divorce in the future, nor by conditioning it on will with a phrase that does not indicate a condition and a consequence. As for the husband's statement "You are divorced with one talaq", this is an explicit divorce and divorce occurs thereby, unless his anger had deprived him of his awareness and control. If intercourse occurred after the explicit utterance, and if it was complete penetration, then it prevents the divorce from taking place because it is an innovative (bid'i) divorce. It is obligatory to act upon what is issued by the Sharia Court or trustworthy scholars after presenting the case to them.