Beyond character names and relationships and a few incidental events, the television series was a large departure from the books. Some instances in which the TV show was factual:
The Ingalls family did have an infant son that died (Charles Frederick Ingalls).
Mary did go blind (though she never married).
Eliza Jane Wilder was indeed Laura's teacher for one term (but did not return because of an inability to control the students).
Almanzo and Laura also had an infant son that died.
Most of the action in the series after On the Banks of Plum Creek takes place in De Smet, South Dakota, where the Ingalls moved when Laura was around 12. That is where she met and married Almanzo.
The Little House on the Prairie mini-series you mention was truer to the book, but still revised for TV. Another movie and its sequel, Beyond the Prairie, was a more accurate account of Laura's life from The Long Winter on, into their move and early years in Mansfield, Missouri.