Okay, thank you very much for you input, I just want to clarify a few things so I do not make a huge mistake somewhere.
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Get the 12v-5v buck converter and solder the wires from the 12v 800ma power supply to Vin and Ground-out on the converter? Would it be better to use a breadboard barrel connector so I'm not cutting up wires and potentially mixing the positive and negative side wires from the external 12v power source?
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Use Vout (5v) from the converter to power everything, including the Arduino. Is Arduino UNO's Vin pin the same as VCC?
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When grounding everything, can I utilize the ground pin on the Arduino? Since technically, the UNO will only have the 5v connected to the Vin pin and no "external ground" from anywhere else.
The 12v-5v converter I'm looking at is something like this.
Thank you all. You have been very helpful.