C. the breeder performs the cross and finds half of the f1 progeny have black fur and half have white fur. what was the genotype of the mouse with black fur that she started with in the p0 generation?

The only way this works is if the 2 parents are both heterozygous for fur color. So each parent is Ff (I'm using F for fur color where F is black and f is white).

The two Ff parents would have had to come from two parents that had FF and ff as their genotypes (so a homozygous black mouse and a homozygous white mouse). 

You can check these by Punnet Square starting with the p0 generation and cross FF and ff; you get all Ff.
Then do another Punnet Square crossing Ff with Ff and you get 50% progeny Ff (black) and 50% ff (white).