Considering all the other toxic chemicals that a typical palette is treated with, I'm not sure the galvanized nails are the wort of your worries.
That's a valid concern, but in theory pallets are marked so that you can identify what they're made of, and some of them are just made of untreated wood. I would imagine that this mostly applies to domestic-only shipments.
I know welding is a BAD idea without a breather, but is a wood fire even hot enough to cause problems?
Yeah, zinc vaporizes right around a mere 500 degrees, you can easily exceed that by burning a stack of pallets. Whoops! Been to that bonfire already.