using Uno to multiplex 200 common-cathode RGB LEDs, not sure about resistors

Thanks for those kind words.

and thus limit the current leaving them and going to the LEDs, correct?

Well it's a theory, rubbish but a theory.

And what about the schematics that use the LED on the cathode?

If you just have one resistor in the cathode the voltage drop across it will depend on how many of the other LEDs are on. So say you turn on the red, then the green, the brightness of the red will drop and the green will com on not so bright. When you turn the red off the green will be brighter. Is that what you want to happen?

By the way if you only turn the LEDs on an off in an RGB LED you only get 7 colours, again is that what you want?