Yes, they have learned to place a bead inside the body of the freshwater mussel, thus being able to achieve larger sizes and rounder shapes.
Being able to get a large pearl faster has several advantages. The pearls don't have to stay in the water for many years to grow large-- and as FWP are farmed, this saves the farmer money. The longer a mussel remains in the water, the greater the risk of loss from storms etc.
The black ones are dyed, as Pareltje said. That is not a naturally occurring color for freshwater pearls. The pink/peach color is natural, as are various shades of lavender.
Bead-nucleated FWP come in a range of quality. The best have smooth clean surfaces, high luster and are fully round.
FWP that are dyed are typically lower quality pearls.