The current in the inverting amplifier circuit
Yes - you are correct.

There is a constant current of I1=Vin/R1=50mA (for R1=100 Ohms and Vin=5V). This current goes through the feedback resistor Rf (because we are allowed to assume that no current enters the high-resistive opamp input).

Therefore Vout=-I1*Rf=-(Vin/R1)*Rf. This gives us the classical gain expression

Vout/Vin=-Rf/R1 .