Well, 'Little House on the Prairie' isn't strictly true. It takes inspiration from historical times but incorporates fictional characters and events to create an engaging narrative.
Yes, it is based on the author's real-life experiences growing up in the Midwest during the 19th century, but some elements might be fictionalized for literary purposes.
A fanfiction on this topic could focus on a new family moving to the prairie where 'Little House on the Prairie' was set. They discover remnants of the old way of life and start to learn about the history of the place. As they do, they are inspired to bring back some of the traditional values and practices that were once common there, like community barn - raisings or shared harvests.
Yes, it is. The book series was based on Laura Ingalls Wilder's life on the prairie. Although it may have some fictional aspects to make it more engaging, the core is rooted in truth.