Is it permissible for an engaged man and woman to meet in a public place without a mahram and without the parents' consent? What is the ruling on their communication via the Internet, and is it permissible for the girl to post her picture showing only her face and hands?

It is prescribed for a man who wishes to marry a woman to propose to her guardian (wali), and she remains a stranger to him until the marriage contract is concluded. It is permissible for him to look at her before the proposal and after deciding to marry, whether with or without her knowledge, or the knowledge of her guardian. This does not depend on their permission. If a man decides to marry and believes that his proposal will likely be accepted, and he wishes to see her outside the home, there is no objection, provided that Islamic etiquettes are observed, such as avoiding privacy (khalwa), the woman adhering to the hijab, not speaking in a seductive manner, and limiting speech to what is necessary. As for establishing a relationship before marriage or sending pictures online, this is forbidden because it leads to haram (prohibited acts) and corruption.