Is it permissible, Islamically, for a young man and a young woman who share feelings of love to continue communicating (via messaging or otherwise) for the purpose of getting to know each other, or to exchange updates regarding the possibility of their marriage, or to exchange photos, whether this is with or without the knowledge of their families, and does the ruling differ after engagement?

It is impermissible to exchange words of love via Facebook with a non-mahram young man, as this is a sin that requires repentance. Conversation between the sexes is not permissible except in the narrowest of circumstances and for a need, while observing Shariah guidelines. Correspondence for the purpose of getting acquainted, as you mentioned, is not permissible because it is a gateway to corruption. It is also not permissible to send him pictures. The marriage proposal does not permit any of that, for the suitor remains a non-mahram to his fiancée until the marriage contract is concluded. The most upright way to get acquainted for the purpose of marriage is to inquire about the other party from those who know him. If your marriage becomes easy, then that is good; otherwise, you must ask Allah Almighty to grant you a righteous husband. It is permissible for a woman to seek a husband or offer herself within the bounds of modesty and proper conduct.