Dark current of PIN photodidoe

There are, no doubt, many reasons why the dark current increased, but to answer the question about whether the diode is broken - badly or otherwise - it's just necessary to measure the current with the diode illuminated. If you're using the diode in reverse-biased mode, measuring the reverse current with various levels of illumination will give you some idea of how its response conforms to the data sheet specifications.

If you're using it in photovoltaic mode, then subjecting it to various levels of illumination and load and plotting its response as a load line will also yield salient data.

In the real world, though, if you've exceeded the manufacturer's maximum temperature spec by what... six or seven times? I'd say you've definitely let the magic smoke out.

I think current output from photodiode towards ADC does matter. If it is too high or low, ADC will be fried or breakdown due to too much current drain.

If you're doing a purely resistive conversion from PD current to voltage, then the PD current flows through the resistor, not into the ADC.

^{simulate this circuit – Schematic created using CircuitLab}

The input to the ADC typically has high impedance (at least kohms), so long as the input voltage doesn't exceed the power supply rails of the ADC device. So not much current will flow into the ADC inputs. If you find you need a load resistor over 1 kohm to obtain the voltage you need, then you might want to re-check this assumption or consider using a trans-resistance amplifier instead of just a resistor for current-to-voltage conversion.