Calculating current in the inverting op-amp
You are correct in assuming that \$R_{in}\$ and \$R_f\$ are in series but the potential difference between them is not \$V_{in}\$ but \$V_{in} - V_{out}\$. So instead of the current being (as you suggest):
$$i = \frac{V_{in}}{R_{in}+R_f}$$
It is:
$$i = \frac{V_{in} - V_{out}}{R_{in}+R_f}$$

Another required equation would be:
$$V_{in} - iR_{in} = AV_{out}$$
Solving these equations you can calculate the gain of the amplifier and if you take the limit as \$A -&gt; \infty\$ you will get the same result as you calculated before.
Thus you can see that you could have saved all these calculations by assuming the gain is \$\infty\$ in the first place and potential difference between its inputs is zero like you did in your initial calculations with virtual ground.