How unfortunate that no place of birth on the church marriage record. I take it nothing for a place of birth on the children's church baptismal, right.
the record is in Latin as is his first name Karolus - Karol in Slovak; Karoly in Magyar.
Why would a mother leave a child who is only 10 years old in America with a stranger? Would a family member not make much more sense. Were you able to find the Karol and his parents on all applicable census? What sort of a street/neighborhood was it where the family lived? Our ancestors went to a place where someone from the family was already residing.