I hate to be pedantic,(:-)) but the Pilgrims were not headed for Virginia as such. They were headed for the mouth of the the Hudson river which is the northernmost point of the Virginia charter. They wanted to be part of the Virginia colony, but not close to the seat of power and regulations.

Potatoes. Who says there were no potatoes? Were they not discovered and taken to England 100 years earlier?

I expect Lobsters are not Kosher simply because whoever wrote Leviticus never heard of Lobsters.