Both statements are well-known in the arithmetic theory of quadratic forms (aka integral lattices).  

The first statement is a consequence of Hermite's bound on the nonzero minimum of an integral lattice: the minimum of a unimodular lattice of rank $\leq 8$ is 1.  

The second statement is a consequence of Kneser's theory of neighbors.  You can find it in the last theorem in O'Meara's book.  It also mentioned that Kneser completed the analysis of the genus of $I_n$ for $n \leq 13$.