What is the ruling on expressing feelings of admiration between a young man and a young woman through public posts and pictures on social media, with the intention of checking on each other, to avoid forbidden private communication, until marriage becomes possible?

You both did well in refraining from communication before the legitimate marriage contract. As for what was mentioned about one of them posting something on their page from which the other party understands a meaning they intend, the advice is to stay away from all of that, lest it become a means for Satan to tempt you to something worse.