Is no carb diet healthy?

Hard to say. Your organs/muscles usually burn glucose ( simple carb) for their primary source of energy. Your metabolism can create glucose from fat, protein or carbs but carbs are more easily converted to glucose. Carbs that convert easily to glucose ( sugar, breads, white potato) raise your insulin faster & trigger appetite which leads to overeating. Complex carbs (yams, beans, peas) convert slowly. .
Low carb diet. Best way to loose weight is to reduce carbs. Not sure you can reduce it to zero however.