The word "tekheiles" actually refers to a kind of blue wool; not the dye itself, but the dyed wool. Most hold that tekheiles must come from the chilazon.
There is the opinion of the Tif'eres Yisrael (stated in his introduction to Seder Mo'eid, kelalei Bigdei Qodesh "hinei") that tekheiles is any colorfast blue wool of the right hue. According to him, the Tosefta's and gemara's insistence on using the chilazon is a historical artifact of that being the only dye of that hue which is colorfast when applied to wool that they knew of in their day. But according to him, with today's chemistry, other dyes would be kosher options.
As far as I know, the Tif'eres Yisrael is unique in holding that opinion. Although some (including the TY) do read the Rambam as saying as much about tekheiles for kohein's clothing, they would still agree that for tzitzis the Rambam requires the dye come from a chilazon.
The "space" of possible colors is three dimensional, so a color cannot be described with fewer than three numbers. Monitors mix primary colors, so you may have seen RGB (red-green-blue) numbers to describe the desired color. Dyes use a very different set of axes: hue, saturation and value (or light). Hue tells you where on the spectrum it is, and is usually described as a circle. (Closing the spectrum by connecting the bottom end and top end at purple / magenta.) Saturation is how much color, and value (or light) is how dark (or light) it is.
Picking a given dye would mean that the hue should be constant. But not the other factors. The amount of dye used would change the saturation and value of the resulting color.
BUT: being told the dye must be extracted from a certain kind of marine animal doesn't mean that all marine animals of that species produce exactly the same chemicals in the same proportions. Just as there is slight color variation among the greens of maple leaves. And perhaps there is a recipe by which the dye is extracted, or attached to the wool. So, it's not even clear that the dye is always exactly the same hue, either.
Nor that there is one kosher hue rather than a range of hues. For example, the Rambam's "color of the sky on a clear day" is not that specific.
As for fading.... The dye must be colorfast. The gemara even offers a test for colorfastness to distinguish between true tekheiles and indigo dyed wool (from the indigo plant, in the tea family of bushes).
That said, fading can also be caused by the dye retaining its color, but being chemically teased off the wool. This is how Woolite works, for example.
As an example of what we expect when we say "colorfast": R/Dr Moshe Tendler reports that when he took murex-dyed wool and left it in bleach, the wool eventually dissolved, leaving the dye as a sediment on the bottom.
