  In this article, we study the hyperbolic Anderson model driven by a
space-time \emph{colored} Gaussian homogeneous noise with spatial dimension
$d=1,2$. Under mild assumptions, we provide $L^p$-estimates of the iterated
Malliavin derivative of the solution in terms of the fundamental solution of
the wave solution. To achieve this goal, we rely heavily on the \emph{Wiener
chaos expansion} of the solution.
  Our first application are \emph{quantitative central limit theorems} for
spatial averages of the solution to the hyperbolic Anderson model, where the
rates of convergence are described by the total variation distance. These
quantitative results have been elusive so far due to the temporal correlation
of the noise blocking us from using the It\^o calculus. A \emph{novel}
ingredient to overcome this difficulty is the \emph{second-order Gaussian
Poincar\'e inequality} coupled with the application of the aforementioned
$L^p$-estimates of the first two Malliavin derivatives. Besides, we provide the
corresponding functional central limit theorems.
  As a second application, we establish the absolute continuity of the law for
the hyperbolic Anderson model. The $L^p$-estimates of Malliavin derivatives are
crucial ingredients to verify a local version of Bouleau-Hirsch criterion for
absolute continuity. Our approach substantially simplifies the arguments for
the one-dimensional case, which has been studied in the recent work by Balan,
Quer-Sardanyons and Song (2019).
