My wardrobe is full of colorful clothes

That's actually really interesting to think about
White light has every color, but white dye has no color.

And black dyes turn purple/other dark colours when they fade

Exactly... it depends on whether we are talking about additive color or subtractive color.

If something is said to be black it means it absorbs but does not reflect any light in the visible spectrum of light. If something is white, it reflects all light

It's going on the "the color of an object is actually every color but the one you percieve" thing, in which cause, if something is black, it's because no color is being reflected from that object to your eyes, and therefore that object absorbs/contains all color. (And white means no colors are absorbed)

Yes that is how it works. When you Break down white you can see every color and when you break down black there is no color to find

Black DYE contains every color because it absorbs all wavelengths and reflects none. Red dye for example, contains every color except red so we see the red being reflected off. White DYE contains no color (but shouldn't it be clear?) because it reflects all wavelengths.
Black LIGHT doesn't exist because there is no color. White LIGHT contains all colors.

That is for how much light the LEDs on the screen will emit

Brown can contain a degree of every color, but black contains 100% of every color.