Whilst it has a large Native American population compared to other states, at 7.9% (per Wikipedia) it's not really large enough to make a big impact for the purposes of this quiz. North Dakota is still very white - 73.5%.
Outside of the Northern Virginia DC suburbs, Richmond, and Virginia Beach/Hampton Roads area most of the state is pretty "white" (not really a thing)... but those 3 areas are where most of the population is so yeah maybe it's a little surprising.
Definitely. African-Americans are the most visible minority because of this country's complicated and often reprehensible history with that group, but Hispanics are a larger group. I think African-Americans make up about 13% of the population, but Hispanics make up almost 20%. Asians are around 5-6%. I think the white population is like 60% of the total population.
My tip is to go into Vicksburg, then take 61-3-49 up to MS-12. You'll see a lot of great scenery.