The resistor and capacitor are "recommended". It will probably work without them but your odds are better with them.
I've usually seen a 100 Ohm resistor recommended but 470 should be OK. The data input on the LED strips is very high impedance so virtually no current flows and there is virtually no voltage drop across the resistor. If the resistance is way too high the LED strips will be more prone to noise pickup and you might get "capacitive" effects.
Adafruit does recommend applying power about every meter so if you get dimming or flakey operation at the far-end, apply power to both ends.
Thanks for the feedback. Here's my horribly drawn sketch. My question is does the 5V and GND from the R3 need to be hooked to anything, and do the wires with question marks on them need to hook to anything.
Do not connect the R3 5V(red wire scribbled). DO connect the R3 GND (black wire scribbled). The signal from the Arduino MUST have a ground in common with the power to the strips.
For clarity, since you have two power supplies for the strips, be sure to connect the GND of both those power supplies to the Arduino GND.