LM358 circuit with Arduino micrcontroller ADC input

int can only be 0-255

That's not correct. In the C programming language, an int is always at least 16 bits wide, even on 8-bit micros. A char is 8 bits wide.

But when using inttypes.h, I strongly recommend using the explicit types like uint8_t,int16_t or uint32_t.

Your real error is using _delay_ms() with a variable parameter. This is not allowed, as it is a macro involving floating point calculations - at least in avr gcc. You are supposed to use something like this:

void DelayMs(int delay) {
  while(delay--) _delay_ms(1);
}

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.