Coconut "oil" is a fat if you're using the regular definition of room temperature. It's solid at room temperature and has high saturated fat content (>90%), even worse than dairy (~60-70%). I know there are some other aspects to it that makes people enthusiastic but I don't think there is any solid evidence that those aspects compensate the huge amount of saturated fat.

You should get about 2x more unsaturated than saturated fats. So dairy, pork and coconut fat should not be a large part of the fat in your diet.

Indeed, olive oil, flaxseed oil, peanut oil, sesame oil and basically every oil except coconut has more unsaturated than saturated fat and will help you balance your fat types.

Source: am vegan and have family with inherited heart/cholesterol problems. I've been reading ingredients and nutritional values on all food packaging for a while now