Thank you for the additional array of images.
When viewing a strand presenting with natural characteristics, we need to consider some things we don't see as well.
Pearl strands are almost never comprised from every pearl in the lot. Instead they are usually selected from a much larger pool based upon subjective criteria and the overall appearance of the collection. In other words, what are the matches? The finest strands may use up to eight points of matching. Natural strands are generally created around one or more match, then rely upon match by mismatch to achieve a desirable symmetry and balance.
I get the impression this strand is from two lots. While there's a distinct graduation, there is an abrupt change in symmetry on the smaller pearls. A middle size range is absent between them (albeit subtle). There are no knots between the pieces. While knots are not conclusive, they are greatly suggestive. After all nobody enjoys watching expensive pearls topple off onto the floor, needlessly.
I see a lot of flat spots and other indentations where these formed in close proximity to other pearls. This is highly suggestive of mussels as opposed to pearl oysters. Keishi pearls rarely do this as those tend to be more singular (and finer) in their formation.
The colours don't match perfectly, but they are within a range of tones. Again, this is where match by mismatch can be applied.
The lustre is somewhat uniform. When combined with the graduated sizes and overall shapes, this is how the strand came to be.
These pearls have translucency revealing nuclear materials. Appearing random, asymmetrical and varied in colour. Cultured pearls tend to be more uniform, but not always.
There is no provenance suggesting natural origin as the items were marketed. Even if these were suggested to be natural, I would still be skeptical because strands like these are not difficult reproduce from a greater pool of freshwater cultural pearls. Having examined elaborate fakes, I see no intentions to that end in this piece. It's quite acceptable to create a piece to give a natural impression.
For those reasons, I suggest cultural freshwater origin with approx 70-80% certainty. That said, there remains a plausibility these could be natural and as such merit a trip to the lab.
It's a pretty strand and I enjoy viewing these types as much as others all the same.
You've asked the right questions. Thank you for sharing them with us.