Problem understanding the operations of capacitor
The current thru a capacitor is the rate of change of the voltage times the capacitance.  At the same voltage, higher frequencies have a higher rate of change (derivative), so a capacitor conducts more current at higher frequencies, all else being equal.

Another way to look at this is to imagine a capacitor driven with different frequencies, all with the same peak to peak voltage.  That peak to peak voltage dictates how much charge is sloshed around each &frac12; cycle.  The higher frequencies will cause the same charge to be sloshed more often.  Charge moving per time is current, so the higher frequency voltages cause a higher current thru the capacitor.

Don't get so hung up on names of how a capacitor is used in a circuit.  Not all uses have short names, so don't try to force one onto every occasion.  Generally bypass capacitor is used for the relatively small and high frequency cap close the the point of use of power.  It's job is to be a short term but immediately responsive reservoir to keep the voltage smooth as the current demand changes quickly.

You can call C1 a DC blocking cap.  I wouldn't try to put a particular name on the use of C2.