  Let $\Delta_\kappa$ be the Dunkl Laplacian on $\mathbb{R}^n$ and $\phi:
\mathbb{R}^+ \to \mathbb{R}$ is a smooth function. The aim of this manuscript
is twofold. First, we study the decay estimate for a class of dispersive
semigroup of the form $e^{it\phi(\sqrt{-\Delta_\kappa})}$.W e overcome the
difficulty arising from the non-homogeneousity of $\phi$ by frequency
localization. As applications, in the next part of the paper, we establish
Strichartz estimates for some concrete wave equations associated with the Dunkl
Laplacian $\Delta_k,$ which corresponds to $\phi(r)=r, r^2, r^2+r^4,
\sqrt{1+r^2}, \sqrt{1+r^4}$, and $r^\mu,0<\mu\leq 2, \mu\neq 1$. More
precisely, we unify and simplify all the known dispersive estimates and extend
to more general cases. Finally, using the decay estimates, we prove the
global-in-time existence of small data Sobolev solutions for the nonlinear
Klein-Gordon equation and beam equation with the power type nonlinearities.
