Your first transformation is correct (it's exactly the same circuit, nothing changed), your second is not. In general, electronic components are only "in series" when there's nothing connected between them.
R5 and R1 both go from V2 to ground, so they're in parallel and you can simplify them to a single resistor (let's call it R51). Next, R3 and R51 form a voltage divider. You can replace it with its Thevenin equivalent.
R4 and R2 also form a voltage divider that you can replace with its Thevenin equivalent. This means that the Thevenin equivalent voltage source is Vin*R2/(R2+R4) and its impedance is R2||R4. It connects to the inverting input of the OpAmp. R6 stays where it is because you can't include it in the Thevenin calculation due to it being involved in the feedback path.
After these transformations, you're left with a voltage source connected directly to the non-inverting input of the OpAmp. The OpAmp itself is connected as an inverting amplifier.