Electronic – How to calculate the maximum amplification of a transimpedance amplifier

You're overloading the amplifier. Recovery from overload can be very fast, but 1 millisecond is not uncommon, and tens of ms is possible even with multi-MHz GBW op-amps.

There are amplifiers such as the OPA380, which has 100ns overload recovery.

I don't see a number for the LF357, you can measure it, as suggested in this classic application note AN356 from Analog Devices.

1. Response is low at low frequencies because \$C_1\$ blocks low frequency signals from reaching the input of the amplfier.

2. Response is low at high frequencies because of parasitic capacitances within the MOSFET. A typical small-signal model of a MOSFET looks like this:

(Image source: QSL.net)

Typically, the most important parasitic for limiting the high-frequency response is \$C_{gd}\$. The gain in the circuit multiplies the effective value of this parasitic, by what's known as the Miller effect.

The main effect of \$C_{gd}\$ is to provide a negative feedback from the output node to the gate node.

Cds can also be important. In an ac equivalent circuit, it is essentially in parallel with the output capacitor (\$R_D\$ in your diagram), reducing the overall output impedance, and thus the gain, at high frequencies.