No, they mean what they say. If a person needs to watch for gluten, then this is pertinent information. And if a person prefers organic food, then this is important information as well. As such, the people looking for this information would probably look at it as healthier food in view of their preferences.
Lower calories? Lower than what? I do not understand the reference here because neither the term ‘gluten-free’ nor ‘organic’ has anything to do with calories.
No, it does not. If an ingredient is a low enough proportion, the product can be labeled as “free” of that ingredient. If you read the ingredients list, you may see that there are small amounts of the “free” ingredient.
Organic can be healthier if it is truly without chemicals, which our bodies do not want.
Always be sure to read the ingredients list to make the choice; and, better still, eat mostly fresh and natural foods that do not need a label or list.