Question

What was the name of the law in which the government gave a 160 acre farmhouse anyone willing to work on or improve the land ?

Answer 1

Ah cool! 

This would be referring to the Homestead Act! They would give the land to anyone who was willing to work on or improve the land. 

The land was given almost free of cost and all the new owner of the land was required to do, was work the land until it was ready for farming/crops, and then they had to build a house for themselves (and possibly their family).