properties of System
For question 1: apply the definition of time invariant: find the output as normal; find the output with the same input but delayed by $T$ 
$$
y_1(t) = \frac{dx(t)}{dt}\\
y_2(t) = \frac{dx(t-T)}{dt}\\
$$
Does $y_2(t) = y_1(t-T)$ ?

For question 2: Find a definition of stability and apply it. For example, for a system to be BIBO stable it needs to have

$$
\int_{-\infty}^{+\infty} \left|h(t)\right| dt &lt; \infty
$$

If $h(t)$ is periodic and non-trivial (zero), can that be true?