ASTM B 6 - 00 Standard Specification for Zinc outlines the requirements for 3 grades of zinc - Special High Grade, High Grade, and Prime Western.  I have no idea if the FDA has a requirement for the allowable grades to be used in contact with food, but here are the chemical composition limits for the 3 grades:

        SHG           HG            PW

Pb    0.003 max 0.03 max   0.5-1.4
Fe    0.003 max 0.02 max   0.05 max
Cd    0.003 max 0.02 max   0.20 max
Al     0.002 max 0.01 max   0.01 max
Cu    0.002 max ----           0.20 max
Sn    0.001 max ----           ----
Non-Zn
total 0.010 max 0.10 max   2.0 max

Is "pure" zinc used in galvanizing or is it alloyed with something (for example to improve adhesion or wear)?  Or, is anything else deposited with the zinc during the galvanizing process (such as a primer type coating)?

There are a number of different processes that are used to galvanize steel.

Often lead is added to prduce a smoother finish.  Aluminum is added to reduce the iron-zinc difusion zone.  Cadmium should be expected as either an additive or as an impurity.

Better answers can be gotten from the International Lead Zinc Research Organization (ILZRO) at Research Triangle Park, North Carolina.

Thanks, I have enough info now.