a) The belief that saturated fat in food causes high cholesterol in our blood, which in turn causes heart disease, was based on faulty/incomplete science and is currently a matter of hot debate by researchers.
b) The limit for what is considered a healthy cholesterol level has been lowered over the years. Many sources say it was due to pressure from pharmaceutical companies. Follow the money.
c) There are certain fats that all the experts agree are healthy. These include extra virgin olive oil, unrefined coconut oil, and the fat in fatty fish.
has more detailed information.