90% of the pre-Columbian population was already wiped out long before Jeffery Amhurst may or may not have tried doing that. Regurgitating trite myths and legends is not particularly helpful in increasing knowledge.
Citation needed. The estimate of pre-Columbian population itself is highly debated, I fail to see how you can so confidently state a number that must be derived from that estimate.
In any case - whether the pre-Columbian population in North America was 2 M or 20 M - the proportion of indigenous population killed by "America", (meaning United States of America) is certainly at most a few percent. Most of indigenous peoples of America lived in Central and South America, and most of the perished cultures of North America (e.g. Mississippian mound cultures) were gone long before founding of United States, and before major English immigration.
The cultures weren't gone. There were still mound building cultures active in the South when Spaniards arrived. Disease most likely played a large factor but to a certain extent it is a mystery. The American policies ensured that there cultures were nearly wiped from the planet. There was no chance for a rebound of population because of the constant disruption due to displacement and forced migration. This is without the warfare which wasn't the primary source of devastation although it was quite brutal at times. There were a large number of promises of land that were never honored. Look at the Wyandotte's removal from Ohio, they were promised 175,000 acres of land in the West but received nothing of the sort once they gave up their last remaining homestead. They had to find a spot to stay with a fellow tribe. This is all documented and the removal of the American Indian was and remains a real injustice and the impacts are still being felt.
It's a well established fact that 80-90% of the pre-Columbian population died from European infectious diseases, often before seeing a single European, since the diseases travelled faster than the people.
This was centuries before the germ theory of disease became mainstream in the late 1800s, and no one on either side had a clear understanding of what was going on.
Divine intervention was probably the most common theory.
Like I said, citation needed. There are still countries in the Americas with either majority or very significant indigenous populations. Were they immune somehow?
No, they had a much larger population to begin with. Life was very hard in North America before arrival of European technology and crops, and populations were small.