Your body will convert fats and proteins to glucose - the Eskimo grew up just fine on an all fish and meat diet.
You do need insulin so that the glucose can get from the blood stream into the cells. The brain takes glucose as its sole energy source. No insulin, no glucose, brain death.
Not true. The body can also operate in a ketosis state, including the brain.
Actually, the heart muscle and kidneys, prefer ketones to glucose as their energy source. The brain does not use glucose as its sole energy source.
Interesting. I've been told repeatedly by nutritionists at endocrine clinics that, unlike all other organs and muscles, the brain requires no insulin to process glucose. Which is why excessive insulin and the low glucose it produces in type 1 is so much more dangerous in the short term than a lack of insulin and high glucose.
Excessive insulin induces all other regions of the body to consume all available glucose starving the brain, and possibly causing a black out. High blood sugar, caused by a lack of insulin (especially in an undiagnosed patient) has no practical effect on the brain in the short term, because the brain needs no insulin to process glucose.