Hi Debra,
Keep Caulerpa's main horizontal stem right around 12" or less. When you cut caulerpa you should only cut it at one place at a time. Caulerpa is actually one giant cell (it's a siphonous or coenocytic algae) so when it is damaged a lot of the cell contents can spew out a wound.
When caulerpa reproduces sexually the entire "plant" turns clear and releases smoky gametes. Shortly after this it dies. Caulerpa does produce some toxins. If a large amount of caulerpa dies or "goes sexual" in an aquarium it can harm the tank. That's why I say keep individual plants small. If one individual dies or "goes sexual" it will only release a bit of toxin. If all of your caulerpa dies or goes sexual it can release quite a bit of toxins and do anything from irritate to kill organisms in the tank depending on how much caulerpa has died, what kind of organisms are in the aquarium, what kind of filtration is on the aquarium, etc.
I think the parts of the caulerpa that turned white were probably damaged in transport. Is this caulerpa in your main tank or in a refugium / algae filter? What kind of lighting do you have the Caulerpa under? Do you test your nitrates and phosphates? If so, what are they? Do you have other algae growing fast?
HTH,
Kevin