They look like cultured akoya pearls.
What is the length of the strands and the size of the pearls? Can you give us any history on the pearls? What they cost, is there a known brand name? How old are they/when were they bought?
Pearl luster doesn't show up well against a black background. Try taking photos against a white background (like a paper towel) without flash, and include some closeups so we can see the pearl's surface better.
Platinum and diamonds will certainly increase the value of the necklace, but we can't tell you what it would appraise at, either for replacement value or resale value (which is much lower than replacement value.) Assuming you own these pearls and wish to sell them, you might want to check the prices that similar strands sold for, either on eBay, Ruby Lane, or other venues. Generally pre-owned pearls do not hold their value well (unless they are documented as a high end brand like Mikimoto) but the fancy clasp will make these more desirable.