Is it permissible to chat online with my female relatives (such as my maternal aunt's daughters) who reside in another country, with the knowledge of both families, and without delving into private matters?

The Sharia has blocked the doors to fitna (temptation/strife), and conversing with marriageable women (non-mahram) is one of those doors, which may lead to greater evils. Ibn al-Jawzi mentioned that conversing with and being in seclusion with marriageable women is a reprehensible negligence that leads to perdition and madness. It is a contravention of the Sacred Law and exposes one’s nature to what it is predisposed to incline towards. Conversing with marriageable women is one of the arrows that strike hearts. Conversing with female relatives (non-mahram) is even more dangerous, because Satan sets his snares in matters that people usually take lightly. Kinship ties can be maintained through their guardians, and conversing with them and engaging in extensive talk is an adornment from Satan. Aktham bin Sayfi advised, "Be chaste, and your women will be chaste; and know that conversing with women is a branch of zina (fornication/adultery)." Abdul-Malik also advised his children’s tutor to keep them away from conversing with women.