They are very definitely cuttable. WS2812 can be cut after each LED - they are powered from 5V, but be warned that they require quite a lot of current, so in the case of an infinity mirror power both ends of the strip to reduce the voltage drop.
WS2811 are powered from 12V and can be cut every 3.
Each LED is controlled by a digital communication, and can be set to display whatever colour - including staying OFF, but still drawing some current for the digital part of the IC. Every LED can have a different colour (that's the point of having individually addressable LEDs).