Mean and variance of a product of the form $\prod_i(1+Z_i)$

Question

I'm working on something involving the following scenario: First fix $k\in\mathbf R$.

Let $Z_1,\dots,Z_n$ be i.i.d. random variables with finite mean and variance.

Also let $X$ and $Y$ be random variables with $$ X=k\prod_{i=1}^n(1+Z_i)\quad\text{and}\quad Y=\prod_{i=1}^n(1+kZ_i). $$ I'm interested in the properties of the difference $D=X-Y$.

In particular, I'm looking for a way to express $\mathbf E(D)$ and $\text{Var}(D)$ in terms of $\mathbf E(X)$, $\mathbf E(Z_i)$, $\text{Var}(X)$, $\text{Var}(Z_i)$, and constants $k$ and $n$?

If not, what if we limit the scenario to the case when $\mathbf E(Z_i)=0$ and $Z_i\in[-1,1]$?

Any insight on this is greatly appreciated.