I don't know Friederich Anderssen-Falch but read from the 1801 Census of Norway that he was a chief pilot. He was living in his second marriage - and Norwegian name tradition indicates that Diane Carine was a daughter from the first marriage. Theory: Diane Carine could have had name from her mother's mother and the second name after her mother's second name. If Karen Mathea was her mother she would have been 17 or 18 years old when pregnant. The second girl was named Else Carine. A theory could be that the first wife died from one or two children, and then he remarried and named the first girl after his late wife - according to Norwegian "rename rules": could have been Else Carine. To me the names indicate that your Friederich Andersson Falch had Swedish anscestors. The two older children have more Swedish names than Norwegian. Hans Broderius and Diane Carine is different from the younger children: Anders Olaus, Jacob Abraham, Mathias (a bit Swedish), Elisabeth Christiane. Finally he had Andreas Lyngblom living in his house - a typical Swedish name. Just theory, but also an indication where to search. I will keep my attention to your family - and hope that you will keep an eye on my Falch-family in US. After the people you mention - my knowledge is zero.