When talking about input and output impedances, what are we comparing them to?
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The impedance of your circuit seen from the input is the impedance of the capacitor (depends on frequency) plus the impedance of the resistor (just R), seen from the output the two impedances are parallel so the impedance is the impedance of the capacitor parallel with the impedance of the resistor. Zc1//R1 calculated as Ztotal^(-1)=Zc1^(-1)+R1^(-1). and Zc1 can be calculated as 1/(2 * pi * f * C) where f is the frequency and C is the capacitance of C1 in farads

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Look up thevenin equivalent, it will help you understand how an output/ input can have an impedance. the impedance is basically just the slope between the voltage and current, if an increase in voltage at an input or output of 1v leads to an increase in current of 0.1A then the input/output has an impedance of 10ohm

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It is important to note that the way the impedance of a capacitor or an inductor differs from the resistance of a resistor is in that they don't dissapate energy due to the current*voltage in them, that is because there is a 90deg. phase difference between voltage and current in capacitors and inductors.