Sometimes the colonists would give blankets to Native American tribes, that were worn by smallpox victims. They knew that it would kill the Natives off, but they did it anyway, so they could have more land.
Incorrect, that was done intentionally many centuries later by the united states.
As far as inoculant goes. The wiki was pretty ambiguous and didn't say what they tried to inoculate in the 16th century. Even then, news did not spread that quickly back then. You have to remember that tv and internet did not exist back then and the only way to travel long distances was by boat. Even that is pretty slow because you have to rely on sails.