Not entirely myths. I think just posting this and walking away from it is a bit of a disservice ... no better than articles that promote the opposite w/out explanation.
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muscle burns crazy amount of calories
Compared to the same volume of fat, muscle *does* burn crazy amounts of calories.

But you have to keep it in perspective. Will you lose 10lbs by building muscle? No, but you will raise your metabolism enough so that your diet will be more effective. Someone who is skinny w/out muscle will have to drop their calories a lot more to lose weight than someone who is skinny-lean with muscle.
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carbs make you fat
Carbs *can* make some people fat. For some people carbs are trigger items. For some people like kaplods, carbs are metabolised differently.
And a statement that "carbs make you fat" is false is kind of disingenuous. Fat doesn't make you fat either. Eating too much fat makes you fat. Carbs don't make you fat. Eating too many carbs makes you fat. Calories don't make you fat. Eating too many calories make you fat. And so on.
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working out on an empty stomach is better
Working out on a full stomach is probably not a great idea. Eating a small amount of food (carbs, and some protein) is a better option. But it's all very personal. For some people any food in their stomachs is a bad idea and will make them feel ill while they're working out. For some people working out on an empty stomach makes them feel ill. There is no "right or wrong" answer here. There is just what is better for each person.
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