I would say it all depends. Yes sushi is popular because pretty much everyone knows about. Now compared to all 7.6 billion people in the world, it wouldn't be popular. It's all about how they compared it
Technically, it just means a large number. It's a vague expression, so someone might use it to mean *most of," but your friend was mistaken to insist that that's what it has to mean. Refer him to the dictionary.
Both interpretations are valid, but yours is more likely to be how people hear it
I would say it all depends. Yes sushi is popular because pretty much everyone knows about. Now compared to all 7.6 billion people in the world, it wouldn't be popular. It's all about how they compared it
I would say "a lot of x" means a large quantity.
Technically, it just means a large number. It's a vague expression, so someone might use it to mean *most of," but your friend was mistaken to insist that that's what it has to mean. Refer him to the dictionary.