Freshwater pearls' nacre thickness is not a quality consideration. Freshwater pearls are composed of solid nacre with an occasional hair-line void in the center that is visible on X-rays.
I have seen certificates produced by retailers of freshwater pearls and Web sites selling them claiming "nacre very thick". This makes no sense whatsoever. It would tell me that there is no real grading going on as quality attributes are simply being thrown around with no meaning. The only way one freshwater pearl has thicker nacre than another is if it is larger than the other. But on a relative basis the nacre depth is exactly the same; whether the pearl is a gem-grade round or a junk-grade lump of chalk.
When bean-nukes become more prevalent (round bead-nukes), nacre thickness may eventually become a quality factor. But that is still a ways off.
Regarding the dye job, I would not worry about it coming off at a party
For the most part, organic dyes are permanent as the compound has been soaked up by the nacre though a process of heating and pressure (like a pressure cooker).
As for the colors, variations are sometimes used, but primarily in darker-color freshwater.
We use a combination of Tahitian colors in ours.
http://www.pearlparadise.com/detail.aspx?ID=1191
This color is custom. You will not usually see color combinations this at tradeshows. Most of the time, dyed freshwater are a single color on a single temporary strand. We mix the different hues to create the multi-hued effect.
Regarding the eBay pearl, the picture is not coming up for me.