And I'm definitely with wvmarle here.
A very real danger is that the obsolete tutorials on the Arduino site and others misleadingly imply that the largely ornamental "barrel jack" and "Vin" connections to the on-board regulator allow a usable source of 5 V power. This is absolutely not the case. It was essentially only for demonstration use of the bare board back in the very beginning of the Arduino project when "9V" transformer-rectifier-capacitor power packs were common and this was a practical way to power a lone Arduino board for initial demonstration purposes. And even then it was limited because an unloaded 9 V transformer-rectifier-capacitor supply would generally provide over 12 V which the regulator could barely handle.
So yes, power the pump with 12 V, obtain a 12V-5V "buck" converter and feed it with the 12 V, connect its output to the Arduino 5 V and ground, and connect its output separately to the relay 5 V and ground with the relay control wire running back along with the power wires such as to form no open loops.
Now that you have adequately powered the relay board and the Arduino, connect your sensors directly to the Arduino. We do hear questions as to how to make the multiple parallel connections needed particularly for power, the answer is that is when you need to learn to solder and why the UNO in particular is inconvenient; a Nano can (with pin headers soldered) be used in a breadboard or soldered on perfboard/ "stripboard" (Vero) for permanent use.