Time-variance and causality of $y(t)=\sum_{k=-\infty}^{+\infty}x(t)\delta(t-kT)$
I agree with you on the system being a causal system since at a point in time $t$, the output is only made out of the input signal at the same point in time, weighted with an impulse (or not).

You can prove its time-variance by showing that a time-shifted input signal yields another output signal than the original input signal, for example:


$x(t) = \delta(t-\frac{T}{2})$ evaluates to $y(t)=0$ while
$x(t) = \delta(t)$ does not.