Question

Over many generations, the fur on polar bears mutated white to help the bears hide better in the snow.

Answer 1

True.
Polar bears evolved from the brown bear. Their fur mutated from dark to adapt to the colder climate and to hide in the snow. Probably, in the past, there were some bears with mutated lighter fur. This trait allowed them to survive so that mutated gene was transmitted to the next generations. Lighter fur allowed them to retain body heat and better to hide during hunting. White bears had a higher fitness than brown bears in the cold climate, so generations later, all polar bears were white.