Question about op amp input capacitor
It is just an AC coupling capacitor.  It prevents any DC component of the input signal from being amplified.  Ra and Rb serve to set the DC input voltage to halfway between the rails.  It is common in any application where the DC component is unimportant, and especially in single supply circuits such as this one, where the "mid rail" voltage is +Vs/2 rather than 0 VDC.  The DC level on the output is blocked by Cout, and the gain at DC is reduced to one by C1.

Because the capacitance is not inside the feedback loop, it does not affect the stability of the amplifier.