Is it permissible for a suitor to add his fiancée on Facebook so that he may see what she posts, and vice versa, for the purpose of understanding the other's thoughts, knowing that they will not communicate through it?

It is permissible for a man to add a woman and vice-versa on public social media platforms, as long as there is no fear of temptation (fitna) and no religious prohibition is present. However, private chats are forbidden, because they are an entry point for Satan and resemble khalwa (private seclusion of a man and a woman who are not mahram), and to prevent temptation. Therefore, it is safer to avoid adding between genders on social media.