Yes. See Lattices and Codes by Wolgang Ebeling. In the second edition, this is Exercise 4.4 on page 134. I do not believe this information was in the first edition; further, there is a third edition now. Anyway, the isometry group, or automorphism group, is generated by reflections in the roots of $L$ and $\pm 1.$ Essentially you use the proof of Theorem 4.6, due to Conway. The same techniques shows that, for any integral even lattice with square root strictly below $\sqrt 2,$ the class number of the lattice is one. In particular, it is not necessary to have unimodularity for this latter result.

Yes. See Lattices and Codes by Wolgang Ebeling. In the second edition, this is Exercise 4.4 on page 134. I do not believe this information was in the first edition; further, there is a third edition now. Anyway, the isometry group, or automorphism group, is generated by reflections in the roots of $L$ and $\pm 1.$ Essentially you use the proof of Theorem 4.6, due to Conway. The same techniques shows that, for any integral even lattice with covering radius strictly below $\sqrt 2,$ the class number of the lattice is one. In particular, it is not necessary to have unimodularity for this latter result.