Dear Anna,

 Please consult

https://sites.math.rutgers.edu/~zeilberg/Hist21/q8S.pdf

for the full solutions.

You got 8 points (out of 10). Here is what you got wrong:

#1: Euler proved it before Laplace, -1 point
#3: Gauss proved it, not Fermat: -1 point




 Best wishes,

   Dr. Z.