Supplying power to both the Arduino and the LED "path" using the same wallwart:Just split the power supply, one line to the Arduino and the other the LED path.
Doesn't hurt to ask. Little time to ask & confirm beats smoking something & losing a lot of time getting replacement parts.
Yes, like the third circuit, except the resistor is outside of the group of LEDs (i.e. the resistor is in series with the group of parallel LEDs).