can I also use phasors/concept of impedances for non sinusodial signals?
If the input signals are not sinusoids, and are not periodic signals that can be decomposed into sinusoids, then you will probably need to do some kind of transient analysis or fall back to differential equations.
The impedance value of a capacitor is only valid at a single specific frequency. Without sinusoids the conventional notion of impedance is not very useful.