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Great, be sure to connect it to the 5V//Vcc pin of the Arduino. If you use a Uno, don't connect USB at the same time. Or set the step down to 7V and connect it to Vin/RAW.
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Bad idea, the Arduino can't deliver the power you need. Use a transistor to drive the pomp from the 12V. Or even easier, a relay module to switch the power to the pomp.