oohhh but haebom's really his dad now since he adopted sungho???

Not a dad but a guardian. When you're adopting someone, you self declare your role in their lives, you can call yourself a parent, a grandparent, a sibling, or simply a guardian which is a general term for non-family members that are responsible of you.

Technically yes but since SK doesn't legally recognize gay marriage, many couples adopt each other to become family. So haebom is legally a parent, but in actuality its a loophole marriage