can I also use phasors/concept of impedances for non sinusodial signals?

analogsystemsrf has already hinted at my cheeky answer: if you need to work with non-sinuoidal signals, rather than a nice sinewave specified by a single frequency, the response of your circuit will be a spectrum, rather than a single "phasor" :-) A spectrum of phasors across some frequency range of your interest... This is because your input signal is a spectrum as well. Fourier Transform works for any signal. The dubious fun begins, where you introduce non-linearity into the circuit. Especially dubious and pointles, if your circuit is some basic digital system, rather than a principally analog signal chain. But if you're actually speaking about analog signal processing by DSP methods, that's a whole different story...

You've mentioned capacitors. If you apply an RC filter to a rectangular waveform, there are two basic cases: you get a low-pass or high-pass filter response. Which means that you suppress the higher harmonics, or suppress the "fundamental"... The link above points to a tutorial site with some static explanation of the maths. If you want something "live" to play with, I suggest that you try modeling stuff in Qucs or QucsStudio.

What is Phasor exactly? If you take an electric circuit, and think of it as a linear system, then the output phasor is the Fourier transform of the network function multiplied by the Fourier transform of your sinus input. As I understand you wish to analysis the circuit not only for sin and cos input. For that, what I would do is analysis the circuit using the Laplace transform.For instant, you want to understand the behavior of RC circuit. Try writing the circuit eq. Apply the Laplace transform of both sides. You can understand a lot by analysing what you get using the Laplace transform properties.

Capacitors always store charge, perhaps for just a few hundred picoseconds during the half-cycle of a WIFI Radio wave in a channel filter, or for 0.1 second or longer in your power supply that can sustain the computer operation during changeover from line_power to battery_backup_power after line voltage collapses. Or, in past decades to hold the requested vehicle_speed in a automobile cruise control, the capacitor holds the GRID VOLTAGE on a vacuum tube or MOSFET, for an hour or so.

Energy in a capacitor can be computed from the charge.

And the current can be computed, from how the charge is changing.

With current, and voltage, we can compute Impedance. Which we use in single-tone circuit behavior prediction.

However, if we map the Impedance, or compute the Impedance over a range of frequencies, we can use Fourier Methods and/or Convolution Method, to predict results of Complicated (real world) waveforms and signals and data sequences and modulations.

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.