Why is my LCD stop to work correctly when my pump is running?
Troubleshooting this type of thing requires an oscilloscope, which I'm guessing you don't have. However, based on your photo and schematic, we can make a couple educated guesses, which might be good enough.

Firstly, you probably want some capacitance across the 12V supply. The supply can respond to changes in current only so fast. A capacitor provides a reserve of energy to help fill in these sudden changes in demand. The capacitor also helps to absorb transient energy spikes such as those that might come from the pump motor.

How big? More is better, until you have enough, then it's just wasted money. Usually an electrolytic capacitor is used, maybe as much as 1000µF. The value isn't terribly critical so use what you have on hand. I'd put the capacitor right where the wire from the supply split to go to the pump and the Arduino.

Secondly, you may need a flyback diode across the pump, if it doesn't have one internally already. If you don't know, it can't hurt to add another. Put this as close to the pump as possible. Put the cathode on the + side of the supply, and the - on ground, such that it's normally reversed biased. If you get it backwards, you will know by the smoke.