Asmodeus is the demon king who came in the realm. Constellations and demon kings cannot just appear in their own bodies, they need 'incarnation' bodies. So Asmodeus is using the daughter's body to appear.
The daughter was born because Han Myungo was cursed by Asmodeus. I think the curse is their greatest fear? And Han Myungo's is apparently giving birth (I'm not sure if I'm remembering this correctly from the novel because it's been along time)
the person answered the rest but I think myungoh was impregnated by that tentacled grim reaper thing from way back then
Is asmodeous the pregnant man’s daughter? And the demon king that appeared in dokja’s realm, is he the one who impregnated the pregnant man