Precisely and exactly said! FK, this is called "typology". The OT is filled with it. the mysterious priest Melchizedek is a type of Christ. A prime example of typology is what we call the "Hospitality of Abraham" from the story in Genesis 18 where Abraham and Sarah provide hospitality to three angels. This is a type of the Holy Trinity. Indeed, the icon of the Holy Trinity is this (this one is the greatest, by Rublev):
Thank you for the icon. I assume the one on the left is the Father? Is there any significance that Christ and the Spirit have their heads tilted more downward than the Father?
I think I've heard of typology, but I still looked it up. :) I suppose I don't have a problem with general foreshadowing, but I would probably draw a line with basing doctrine solely or mostly on IT. Seems to me that would be working backwards. I could employ typology with the virgin in Isaiah 7:14, but I wouldn't assign any extra-special significance to her because of the comparison to Mary.
I would imagine that someone could take "anything" and make a big deal out of it, claiming a new doctrine or truth. One example I saw was that when Moses raised his hands while fighting the Amalekites, the Israelites were winning. This was compared to Jesus' hands being raised on the cross, and the victory that meant. I could say "that's interesting", but I would not go so far as to say it means Jesus was the new Moses instead of being the new Adam. This is what I see happening with the promotion of Mary as the new Eve and co-redemptrix. Creative typology could be used to connect anyone to anyone.