Kerala is sub-set of India and they have one the better socio-economic indices in India, from that my guess is better Health indices relatively speaking. The biggest problem in the state for Health is alcoholism (to my knowledge).

When it comes to food, I follow Micheal Pollen's rule, food that your grandma recognize a.k.a traditional food. Coconut Oil has been used in traditional foods in many parts of the world that is sufficient evidence for me.