All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu 'alayhi wa sallam, is His slave and Messenger.
This is not considered Khul’ (divorce requested by the wife and obtained in return for some form of compensation) just because you asked your husband for Khul’. If this divorce was not issued in return for compensation, then it is not considered Khul’; rather, it is a divorce. In this case, it is incumbent on you to observe the ‘Iddah (waiting period) of a divorced woman, namely three menstrual periods. Assuming that it is Khul’, the majority of scholars held that the ‘Iddah of the woman in case of Khul’ is equal to that of a divorced woman (i.e. three menstrual periods), contrary to some scholars who held that in the event of Khul’, the woman observes ‘Iddah of one menstrual period only. It is more cautious to follow the opinion of the majority of the scholars in this regard.
If what you mentioned about your husband chatting with female other than one's Mahram (permanently unmarriageable kin) women and engaging in sexting with them is true, then this is an evil act on his part. The sin is even graver in his case because he is married; the punishment of a married adulterer is harsher, and this is why the Hadd (punishment prescribed by Allah) of Zina (fornication/adultery) for a Muhsan (one who is married or was once married) person is stoning to death, whereas the Hadd for a virgin adulterer is lashing. However, you should have given him advice instead of hastening to ask for Khul’ or divorce.
We would like to point out that the Muslim scholars held different opinions regarding the ruling on pronouncing three divorces in one single utterance. The majority of the scholars maintained that it counts as three occurrences of divorce. The chosen opinion by Ibn Taymiyyah was that it counts as one occurrence of divorce.
We would also like to underline that a woman should reside with her husband wherever he resides, as this helps them maintain their chastity and wards off Fitnah (temptation), especially in those environments and societies where immodesty and the display of nudity are prevalent.
For more benefit about Khul’, please refer to Fataawa 89039, 297739, 131953, 276691, 205168, and 168545.
Allah knows best.