What you precipitated is mostly magnesium, and unless you need milk of magnesia, its of no use.
The idea of dripping sodium hydroxide into sea water is really lame.
Almost every metal will precipitate out at pH10, its one of the ways municipal water treatment plants remove metal ions to purify water.
If I remember the process correctly, toxic metals are not supposed to precipitate until the pH is higher, but the fallacy is that the pH where the drop of sodium hydroxide enters the water is always above that magic number regardless of the pH of the bulk water.
I have in fact tried this procedure a long time ago, only I used salt from the Dead Sea. I got a lot of white precipitate, but it wasn't monoatomic anything.