The Story of Kullervo

Tolkien's earliest surviving prose retelling of a myth -- a version of the Kullervo story from the Finnish Kalevala, written around 1914. It was published posthumously in 2015.

The Children of Hurin character Turin Turambar is consciously modelled on Kullervo. Both are cursed heroes of great strength driven by inevitable doom, enslaved, and ultimately destroyed by fate. The Story of Kullervo is the first draft, so to speak, of what became The Children of Hurin.

No -- editor Verlyn Flieger provides extensive context. However, reading the Kalevala version of the story alongside Tolkien's retelling is illuminating.

No -- Tolkien's prose version breaks off before its conclusion, following the same fragmentary pattern as many of his works. The published edition includes his lecture notes and commentary which fill in the complete shape of the myth.

No -- it is a retelling of Finnish mythology, not a Middle-earth story. It is significant as the source material for a Middle-earth narrative (Turin Turambar) rather than being set in Middle-earth itself.