Time-invariance, causality and stability of $h(t)$ of four given systems
You should remember the necessary and sufficient condition for (BIBO)-stability of a system described by an impulse response $h(t)$:

$$\int_{-\infty}^{\infty}|h(t)|dt&lt;\infty\tag{1}$$

If you use condition $(1)$ you will find out that actually only one of the four systems is stable.

The question about time-invariance does not make much sense, because if we assume that the systems are characterized by their impulse response then we already imply that the systems are linear and time-invariant. For linear time-varying systems you would need a two-dimensional impulse response, and non-linear systems cannot be characterized by an impulse response.