Why is Iron very rare in seawater compared to many other elements?
I'll elaborate this answer as I learn. 

It's an effect owed to the low solubility of iron in the modern oxic ocean and the tendency for iron to be ‘scavenged’ from the water column by sinking particles.

Brand, L. E., Sunda, W. G. &amp; Guillard, R. R. L. Limitation of marine
phytoplankton reproductive rates by zinc, manganese and iron. Limnol.
Oceanogr. 28, 1182–1198 (1983).

Cooper, L. H. N. Iron in the sea and in marine plankton. Proc. R. Soc. Lond. B
118, 419–438 (1935).

Goldberg, E. D. Marine geochemistry. 1. Chemical scavengers of the sea.
J. Geol. 62, 249–265 (1954).