ESC->UNO:
GND->GND
DATA->1
Doesn't make sense apart from GND->GND.
The 3pin connector has ground, 5V and data.
Connect ground to Arduino ground and data to the relevant Arduino pin.
You might want to connect the 5V to Arduino 5V if you are powering the Arduino this way,
but for now run the Arduino off USB and don't connect the 5V from the ESC.
Once everything is working, double check the ESC is outputing clean 5V and then, yes
you could power this way.
I certainly don't recommend it though, the amount of noise may be excessive, and I've seen
ESCs fail spectacularly.