Short answers, pulled from the story.
Daniel Freeman filed the first claim under the Homestead Act of 1862 in Nebraska shortly after President Abraham Lincoln signed the bill into law on the 20th of May 1862. The act officially went into effect on the 1st of January 1863.
The Preemption Act of 1841 allowed settlers to claim up to 160 acres of federal land for $1.25 per acre. It required residents to live on the land for at least 14 months before gaining permanent title.
Women and immigrants who applied for citizenship were eligible to file claims under the Homestead Act of 1862. Black Americans participated through the Southern Homestead Act of 1866 which explicitly encouraged their involvement.
A massive influx of new farmers combined with inappropriate cultivation techniques led to immense land erosion that contributed directly to the Dust Bowl of the 1930s. Farmers accepted marginal lands that could not be easily irrigated yet planted crops unsuitable for the region.
Elizabeth Clouse-Smith became the last woman to successfully prove up land in her own name in Alaska on the 18th of October 1984. This event marked a significant endpoint for women filing homestead claims independently.