How can I evaluate the following involving dirac delta functions?

Question

\begin{align} \delta(x)\delta(x) = ? \end{align}

\begin{align} \delta(x)\delta(x-a) = ? \end{align}

\begin{align} \delta(x)/x = ? \end{align}

In the above problems, a is a real number and a $\ne$ 0, My solutions are below, but I am not sure of them.

\begin{align} \delta(x)\delta(x) = \delta(x=0) \delta(x)=\delta(x) \end{align}

\begin{align} \delta(x)\delta(x-a) = \delta(x=a) \delta(x-a)=0 \end{align}

since the $\delta$(x=a)=0

\begin{align} \delta(x)/x = ? \end{align} I am not sure of this.

Thanks for your feedback.