  We consider Gaussian Laplace eigenfunctions on the two-dimensional flat torus
(arithmetic random waves), and provide explicit Berry-Esseen bounds in the
1-Wasserstein distance for the normal and non-normal high-energy approximation
of the associated Leray measures and total nodal lengths, respectively. Our
results provide substantial extensions (as well as alternative proofs) of
findings by Oravecz, Rudnick and Wigman (2007), Krishnapur, Kurlberg and Wigman
(2013), and Marinucci, Peccati, Rossi and Wigman (2016). Our techniques involve
Wiener-Ito chaos expansions, integration by parts, as well as some novel
estimates on residual terms arising in the chaotic decomposition of geometric
quantities that can implicitly be expressed in terms of the coarea formula.
