Brick walls and issues

These families/individuals are next to impossible to solve:

Issue with birth before church records
My father’s mother was Betty Charlotte Pedersen (1892-1941), who’s father was Anders Pedersen (1839-1896), who’s father was Peder Madsen (1800-1887), who’s father was Mads Pedersen (1776-1846), who’s father was Peder Lauritzen (born around 1750, died between 1776 and 1801). His father was likely Lauritz Andersen, sometimes mentioned as Lauritz Andersen Kræmmer (estimated 1720-25, died?). His father was likely Anders Lauritzen (est 1676, died 1759), who was married in 1693 to Karen Eriksdatter (Erichsdatter), who seems to be born 1682 in Hårby, Veng, Hjelmslev, Skanderborg. The issue is that she cannot have been married 11 years old, so was she born earlier, or is she the wrong wife? I guess I will never know. I have searched the probates to no avail.

Issue with unsolvable paternity
My great grandmother Marie Petersson (1875-1950) divorced her first husband and married Peter Christian Petersen (1882-?) 30 November 1917 in Copenhagen. Peter’s mother Ane Margrethe Pedersen (1850-?) worked in the kitchen at Amalienborg, and told her son that his father was King Frederik VIII, who also paid for his education as a silversmith. As these “incidents” in the royal family were never recorded, there is no way to confirm this.