I have been working on a similar project. There is a ton of pitfalls you are going to have with your 555 design. I'll try to point you in the right direction.
The 555 won't run stable because the capacitor is temperature sensitive. If you look at the capacitor datasheet, most are +/- 30%. Even the best ones have too much of a fluctuation to be accurate. You must measure the capacitor on the RC circuit before each measurement and calculate the real capacitor value.
The pic your using has voltage comparators. You can use those to do away with the 555.
Connect a GPIO pin to the probe, probe to capacitor / comparator, cap to gnd.
Also connect another GPIO pin to a precision resistor to the cap to do the capacitor measurement. (leave the pins in high impedance state when not in use)
So set the pin to high, count clock cycles until the comparator triggers at 2/3, switch the comparator to 1/3, set pin to low, count until comparator triggers. Repeat and average like 10,000 times. Keep it above like 5khz it must be as even as possible. If its too slow put in smaller cap. Also keep a eye on the high/low values... if they are too far apart, the probe is dirty or your having polarization issues. You will need a crystal to get accurate counts as well.
Put a resistor in parallel with the probe to do a calibration when probe is dry. You can also put one in series and short the probe to get a second value to do a y=mx+b calibration.
Once you have your ohms reading. You calibrate with 1000ppm (1 gram of salt in distilled water) and calculate the probe constant K. Conductivity = ohms * K. Also note that EC calibration is only 1 point! The conductivity of 0ppm is infinite.
Also you will need a probe with a thermistor to get a accurate temperature reading. TDS readings are highly temperature sensitive.
Temperature compensation is tough. It's too hard to calibrate the temp, and apply that to your ec calibration and expect anything to work out. Here is my solution: I take a 1000ppm sample, heat it covered in the microwave. I put it in a bowl of ice and record the ADC reading from the thermistor and EC reading as it cools down. From that I build a table of +/- percents to offset at every ADC value.
You will want to isolate the PIC with a dc/dc convertor and a few optocouplers. Especially important if you have other probes connected in the same environment. If its just the single probe you can use a heavy wall wart adapter with a proper transformer in it. Ground loops are a serious pain. I even isolate the temperature sensor, as it can throw off readings if there is a small ***** in the probe.