How to find input impedance of this OPAMP circuit?
When you do the feedback calculations, you need to do the calculation on the amplifier with feedback.  This means that the input impedance you use is the input impedance of the amplifier with the feedback network added.  So the raw amplifier has infinite input impedance and zero output impedance, but as it's used in circuit, the amplifier has an input gain of R2, because there's a path from the input pin to the output.

Then the input impedance of the amplifier + feedback is \$\lim_{a \to \infty} \frac{R2}{a}\$, and it all makes sense.