Lower-grade freshwater pearls have distinct potato like shape to them. The pictured strand looks like the thousands of others hawked in the Zhuji market open atrium for little of nothing per strand. These freshwaters are typically drilled through the width. Tahitian baroques are nearly universally drilled lengthwise. I have seen Tahitians drilled like these CFWP in the past, but they are pieces hawked by street vendors in French Polynesia, and are usually placed on a stretch bracelet. But even those pearls almost never exhibit the classic potato shape so common with freshwater. They almost always have a slight drop shape, and if not it is usually a "stubby" look with concentric rings. It also states that the pearls are 10mm, but the accent pearl is 15mm. The accent pictured appears to be no larger than the pearls in the necklace.
Finally, you can tell they are dyed because they are freshwater pearls. Naturally black freshwater pearls do not exist.
Regarding the "natural" strand, you are right. Looks much, much too round to be natural. Also, the seller is intimating that it is from Europe (Victorian Period from 1830 something to the turn of the century). I think the "Victorian" term is only used because of the clasp, although it does not look like the classic "Victorian" style to me, although this is not my area. A necklace like that would have a lot of history attached to it as well as a hefty price tag. The strand does look old, as you can see it has yellowed. It may only be 15-20 years old, however, if it were not properly cared. I would say the chances of this are much higher than the chance of it being a natural strand.
