Is it permissible to divorce due to incompatibility and differing understandings and ideas resulting from different backgrounds and customs, as well as the wife's lack of knowledge in cooking or managing household affairs?

If harmony is not achieved between a husband and wife, divorce is permissible. However, it is preferable to be patient and strive to remove whatever disturbs their marital life, based on Allah's saying: (And live with them honorably. If you dislike them, it may be that you dislike a thing and Allah brings through it much good) [An-Nisa: 19], and the Prophet's ﷺ saying: "A believing man must not hate a believing woman. If he dislikes one of her characteristics, he will be pleased with another."