I made some great progress on my great-grandmother's (Elisabeth Linnemann) family in the past few months, thanks to some documents I received from Germany. It started with her birth records and those of her siblings, which gave me the names of her parents. I also learned that her mother (Elisabeth Nilkowski) was married to Christian Fasel before she married Gerhard Linnemann. Christian died shortly before their son, Christian, was born. I requested the marriage records for both of Elisabeth Nilkowski's marriages from the city of Gelsenkirchen (where all of the children were born).
No record was found for Elisabeth and Gerhard Linnemann, so I will need to still keep digging there. Below is the record for her marriage to Christian Fasel.
I have asked someone to translate it for me and I will post the full translation when I receive it. What I think I have deciphered is that Elisabeth Barbara Nilkowski was born near Marienburg, which is currently in Poland in what was the former West Prussia Province. It looks as if her parents live in Braunwalde, near Marienburg. If this is correct (my German translation isn't great), then I can look further into her side of the family in Poland. Her husband, Christan Fasel, would not be one of my ancestors, but it does not look like he is from Poland, but from near Montabaur which is in the Rhineland-Palatinate state.
Here is a picture of Elisabeth Nilkowski Linnemann taken around 1903 or 1904 in Gelsenkirchen. Her husband Gerhard left for America in 1903 before she and the children followed in 1904. In the picture with her are her children Christian (Fasel), Gerhard, Wilhelm, Georg and Elisabeth.