just basically no on both questions
if a large plant mass can spend time in the dark, it respires and can drop pH, but not with 24/7 lighting
unless the caulerpa is dying faster than it is growing it is actually reducing nitrates.
you are probably generating nitrates via fish and fishfood.
IMO you should tear out your caulerpa. they're made of large cells and when you cut them the stuff leaks out. cut a lot, a lot leaks out. the growing runner tips grow better. pull it from the bottom of the wad, or wherever it looks the grungiest. leave the healthiest stuff to keep on cooking