Caulerpa, when allowed to grow rampant, will go "sexual" in that it reduces itself to spores in order to reproduce. This works fine in the ocean but is a nasty pollutant in our closed environments. When this happens your tank is in danger of being dangerously low on dissolved oxygen as the cellular algae eats it all up.
Keeping your macroalgae pruned or trimmed back will prevent this. It is also how you remove nutrients from your tank. Regular harvesting (and disposing) of caulerpa is a very effective way to "export" nutrients out of your tank to prevent cyanobacteria and microalgae.
To get rid of the hazy water, do a large water change and filter with disposable mechanical filtration media like a bag of floss in a powerfilter.