  In this paper, we explore the complex symmetrical characteristics of weighted
composition operators $W_{u, v}$ and weighted composition-differentiation
operators $W_{u, v, k_1, k_2, \ldots, k_n}$ on the Hardy space
$H^2(\mathbb{D}^n)$ over the Polydisk $\mathbb{D}^n$, with respect to the
standard conjugation $\mathcal{J}$. We specify explicit conditions that confirm
the Hermitian characteristics of the operator $W_{u, v, k_1, k_2, \ldots, k_n}$
and describe the conditions necessary for it to exhibit normal behavior.
Additionally, we identify the kernels of the generalized weighted
composition-differentiation operators and their corresponding adjoint
operators.
