Can humans transdermally absorb minerals from ocean water, and if so how much?
There is not very much transport of ions or water through the upper layer of the skin, mainly responsible for that is the stratum corneum (SC). Through this layer you will get only with small lipids and also substances which are able to penetrate the lipid layer of the cells like chloroform or DMSO. I think therefore that it is pretty unlikely that you can take up noteworthy amounts of ions (which would have to pass through the lipid layer of the cells which is highly hygrophobic) through the skin. Have a look at these publications:


Routes of ionic permeability through mammalian skin
Skin permeabilization for transdermal drug delivery: recent advances
and future prospects.


Interestingly this is different for other animals. The pacific hagfish is able to resorb organic nutients through his skin, see this article or this publication:


Adaptations to in situ feeding: novel nutrient acquisition pathways
in an ancient vertebrate