What is the ruling on repeated marriage and divorce online with a Muslim woman who is a previously-married non-virgin, without the presence of a legal seclusion or informing her family, and are the three divorces considered a final and irrevocable divorce for the wife?

Marriage is not Islamically valid unless its conditions and pillars are met, such as the guardian, witnesses, offer, and acceptance. What transpired between the questioner and the woman is not considered a valid Islamic marriage. Therefore, he must repent to Allah and abstain from forbidden relationships.