As I said before, it is a trans-impedance amp. Whith the trans-impedance gain of Rf. The designer want to minimize input leakage/bias current by using a J-FET as input. The FET invert the signal, that is the reason it drive the +ve input of the op-amp. The output drive Rf back to the input.
This circuit is nothing more than something like an inverted gain op-amp circuit. As I told you, for the speed you want, you can use any J-FET input op-amp and be done with it. Cheap J-FET input op-amp like TLO81 will be more than good enough for this purpose. You are limited to about 100 Hz only. Form the last circuit, there is a big 100pF from input to ground, that show already there is not high speed requirement. In the last circuit, the Rf is only 1M which meant the trans-impedance gain is very low! There is nothing that is pushing the technology here.
This is the circuit with single J-FET input op-amp. I put a 50 ohm resistor to separate the parasitic capacitance of the detector from the input of the amp to guarente stability. Rf is the same as in your circuit. You should use +/-6V or higher as supply. Cf can be adjusted to get the frequency response you want.
You cannot test these amps but driving directly from the signal generator, this is common mistake when people work on trans-impedance amps. If you drive directly from the output gain would be very high because the output impedance of the generator is 50 ohm. YOu , it will give you gain of Rf/50 in your circuit or Rf/(50+50) in my circuit. Trans-impedance means you put current in and get voltage out. In your case, you expect about 100mV out, if you consider Rf is 1M, then meaning the max input current is I=0.1V/1M = 100nA. So you put a resistor of 10M from the generator to the input and set the generator to vary from 0 to 1V to get your input requirement.
The key to testing a trans-impedance amp is to use resistor to turn the voltage into current before driving into the amp. The 50 ohm I put in series with the input with separate the input capacitance from the detector diode ( most photo detectors are diodes type) to guarante stability of the trans-impedance amp.