I think the answers basically are yes, yes, yes.
I believe Caulerpa does uptake nitrogen in some form, possibly phosphates too -- I know it is great for exporting dissolved organics from the water column. However, tangs will/do eat most species of it much faster than the Caulerpa can grow (and some species, especially the grape racemosa, can grow REALLY fast). My Hippo tang cleaned up all my Grape and Feather Caulerpa from my main tank in short order. He doesn't eat the Sawblade Caulerpa or the Spaghetti Algae (chaetemorpha sp?) though. If I didn't have a refugium/sump to keep my Caulerpa tang-safe, I'd consider trying some Spaghetti algae.
FWIW,
Mariner