Answer to Question 1
From GmM/r2 = mv2 / r where m,M are lunar and Earth masses and r distance from Earth to Moon; he got period T = 2 r3/2 / (GM)1/2.
But he knew g=GM/R2 where R is Earth radius, so
T = 2 r3/2 / (gR)21/2 and he knew g, r, and R.
Answer to Question 2
A