How does a capacitor block only DC and allow AC to pass through in a superimposed signal?

I have read that if we mix AC with DC, the resultant is a wave shifted upwards. i have two questions regarding this:
1. what does this mixed signal look like, how is it any different from a pure AC signal, other that the shifting upwards?
2. how does a capacitor separate the DC element out of the signal. how does it "know" what is the DC element, as it is just a wave?is it true that the mixed signal is a mixture of different current frequencies in the wire?

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First the mixed signal looks just like an AC signal except shifted upwards so that the center is at the DC voltage and not zero.As to how a capacitor "knows", this gets back to what a capacitor is and how it works. Here is a series of tutorials on capacitors that should explain it.
https://www.electronics-tutorials.ws/capacitor/cap_1.html

i know the basics of capacitor, what i was not able to get it is how does the "mixed signal" exist inside a wire, in terms of electrons flowing. in some other forum, someone said that it has to do with harmonics and it is really an abstract idea related to fourier transformations.
as to how the capacitor separates DC from AC, as i now understand, the DC signal charges the capacitor to certain voltage, and then the AC signal charges and discharges it, causing the current to flow in the circuit, because " there will be continuous polarization and
depolarization in each cycle causing rate of change of charge stored in the
capacitor and hence flow of current with a 90 degree phase shift with the
applied voltage."

I think you have the basic idea of how it works.

It takes a while for a capacitor to charge up so if it is connected in series with the signal the DC part (the zero offset -- either up or down) eventually causes the average voltage across the capacitor to match that offset voltage which brings the DC portion of the output voltage to zero.  By the same token, since it takes a while to charge the capacitor, the output voltage tends to follow the input voltage changes especially faster ones.  With each change, it charges a little or discharges a little, but mostly its output matches the input voltage for a short amount of time.  Thus the varying part of the signal passes through the capacitor to the output.   Essentially, the capacitor blocks the DC portion from getting through while it conducts the AC portion right through.  
This phenomenon makes the impedance of a capacitor nearly infinite at zero frequency (DC) and nearly zero at high frequency (AC) so it can be used to filter out either low frequencies (as above) or high frequencies.  When connected in parallel with the input through a resistor (i.e., a resistor from the input to the capacitor then to ground, the capacitor will tend to conduct high frequencies to ground and allow only low frequency voltages to appear across it.  This is the opposite effect of the above series connected capacitor.  Now the DC portion appears at the output but the high frequency portion does not.  Depending on the ratio of capacitance to resistance the frequency below which gets through and above which does not can be selected.  This is called a low-pass filter.

The current that flows through the dielectric of a capacitor, is Maxwell's displacement current.