Hageman is an old FC name oft aligned with Wycoff and the other Dutch settlers in or near Fairview. It is in my tree, but not a primary name; I don't know enough about them to be of much help. You'll find several names with this spelling in Vol. 4 of the Fulton County Cemetery Inscriptions of Fairview and Joshua Townships that is published by the FC Historical Society.
I can say the same about Foster; I don't know much about them. Eunice Foster was my grandmother's cousin. As far as I can determine she was Eunice Martindale who married David Foster. I haven't tried to prove it, but if it is true then her parents were David Miles Martindale and Elizabeth Warfield. David's father Elijah Miles Martindale descends from Martindell the Bucks County, PA Cordwainer who took land after the RW ended. Elijah's father. a minister, died in Indiana. Elijah was the only Martindale I ever heard of who set foot in Illinois - especially in the 1800s. Elijah married Julia Ann Coons, She then married a Mr. Smith after Elijah died unexpectedly.
Coons is a minefield to research as the father David Coons had three wives and children by each. Julia Coons Martindale had 12 siblings that were full sibling, half-sibling, or step-sibling and nearly twelve children of her own.
My great-great grandfather was Edward Foster. He was born in Maryland. I am a product of his first marriage with Mary Mercer. Any chance you are part of that Foster line?
I am descended of Edward Foster. His son was Amos D. Foster, whose daughter, Sarah Margaret (Foster) Maxwell was my great-grandmother. I don't know if Amos Foster's mother was Mary Mercer, though.
Amos was the son of Edward and his second wife Sarah A. Mercer. Mary Mercer was my great-great grandmother, Edward's first wife and Sarah's sister. Amos lived with my great grandfather, John Henry, during his teenage years.