Hi,
I've had a quite similar problem using a "pro mini" (chip is the same). It has to do with the output impedance of the sensors: it should not excess 10 kOhm (desirably 5 kOhm). Otherwise, not only the AX to which the -defective- sensor is attached, but all of the other analog inputs started to give wrong readouts.
If the water level sensor is causing the problem, the academic advice is to connect it through an impedance adapter. I'd rather look for a different one (sensor).
Any case, you have to determine if the level sensor is causing your problem (The LM35 is correct). Perhaps trying with a potentiometer to test ...
A 100 nF in every analog input will help too (and a 4,7 kOhm resistor forming a RC filter).
Saluti