yes, the baby would be a citizen
If she were to get caught (and personally I hope she would), there is a very real possibility that the US would send her and the baby back to her homeland. They baby would be a US citizen and could come back when of age; or the woman can try to come back to the US legally with the child.
Yes, since the mother is a citizen (no matter how she became a citizen), the baby is a citizen regardless of where it was born. However, there are additional rules if the baby does not end up living back in the the US or if the parents/grandparents have not lived in the US for a period of time. Check in with the local embassy.
Only if the baby has reached the legal age, i believe is 21
only if the baby was born in the us
Her child is definitely a US citizen which the baby's birth certificate proves it. but the mother cant apply for residency.
if the baby is born in Korea then the baby will be a citizen of Korea......but can also later become a citizen of the us
we can only hope so
YES!
No.
The baby would be both a US citizen as well as a citizen of whatever country they were born in.
No.
the baby is concederd an American citizen too because it is born in the u.s and it does not matter if the father is not a citizen the baby can still get benefits!