They look like imitation pearls. The findings are not those of Mikimoto but many fake pearls are finished that way.
The pearls themselves don't look real.
Look closely at the drill holes of the smaller pearls on the end where there are a number of small pearls. See that protrusion of coating near the drill hole? That is indicative of a fake pearl coating.
Magnified, the pearls have the coarse surface appearance of fakes.
They are too uniform in color and luster. This also points to their being fake.
They look like a fun strand to wear, though.
If you are looking to sell them, check eBay to see what similar strands of imitation pearls have sold for recently. Look at completed sales. People do buy nice imitations, but the value will not be high.
As for the box...any pearls can be placed in any box, sadly.