"I can't do a lot about the last one. The project requires a simple, single socket power supply. Even if I provided two, very few users are going to plug two in; I know there are things like lipo packs that could be used, but the project is limited in both space and cost, so would not accommodate them."
You can probably get away with just the "single socket power supply" if you make the proper connections. It's important to understand that wires are also resistors. The only things that makes a wire a "wire" is the fact that it's resistance is usually MUCH higher than anything else in the circuit. And, because of this, you can usually ignore the resistance in a wire. But, in cases where a wire is carrying a significant current, that resistance can have a significant impact on the performance of the circuit.
The above figure shows how current surges, caused by changes in the LED currents in the WS2812B devices, when flowing through the wire that supplies these devices, results in a varying voltage drop across the length of the wire -- in other words, noise on the VCC line. If the Arduino is connected at the point where this noise is greatest, it can result in erratic behavior in the Arduino.
A more "proper" way of connecting the strip and the Arduino to the one supply is like this:
I forgot to include it in the diagram, but the ground connections should be done in a similar way (I usually do a copper pour on a PCB for the ground connections, so I forget to think about his.)
C1 is optional. If you have a scope, have a look at the VCC line and if there's a lot of noise, try adding various values of capacitor until the noise abates -- you probably won't be able to get rid of all of it, and I'm attempting to use "small words" so perhaps erratic behavior is your "test" of how much (or if any) capacitance is needed. Also, doing something like a 1000uF in parallel with a 0.1uF can make a big difference, for reasons that are probably too complicated to go into here.
do need the resistor (470 ohm?) on the data line.
You may not need it, but again, the test is erratic behavior. The resistor might be the solution [it has to do with transmission lines and reflections -- i.e. big words].
I don't need decoupling capacitors as the strip has them built in.
If this is a pre-made WS8212B LED strip, then it almost certainly has the decoupling caps already installed.
I think these lights are always in parallel, yes? Even though one might initially think a long strip would be in series?
They are both. And I think the confusion might come from them being called "LEDs". They are not individual [discrete] LEDs. They are RGB LED Modules with an Integrated Addressable Driver. Calling them "LED"s is shorthand.
The Power lines are a parallel connection, but the data that controls them is serial. Thus, the data lines are serially connected. That's important to know if you ever want to connect more than one strip in a way that they are all controlled by the same serial line. DOUT of one strip connects to DIN of the next strip (that's assuming the strip provides a "DOUT"). And, VCC of the one strip connects to VCC of the next strip, and the same with GND.