Is there a difference in nuance if I omit 'self-' in this sentence? I think it's better to use 'conscious' or 'aware' when talking about general things like environmental issues.

Why was "threefold" used here not "three"

"Threefold" means three times as great or as numerous, or to be triple the amount. Here, the speaker has used "threefold" to mean that the meaning to the box is tripled, and to signify or emphasize the plurality of the box's meaning. Just using the number "three" only signifies three items and would have a lesser, more simple effect. Ex: The earnings of the company have increased threefold in the last year. Ex: The significance of the new law will be threefold: it will not only reduce air pollution, but also expand the transportation infrastructure and increase city revenue.

I assume the word "Poseidon" is Greek, while Romans used "Neptunus." Then, which name is more commonly used in modern English?

Oh, interesting question! I've mostly heard "Poseidon" rather than "Neptunus," so I'd say "Poseidon" is more common in modern English.

What's she mean by "later I think?"

She means that it would be possible later. At first, she says that she thinks it would be possible later, but then she says that it would be perfect later. You can use this phrase to recommend a later time for a meeting or appointment. Ex: A: Are you free at 5pm? B: Later, I think. A: How about 7pm? B: Yes, that's perfect! Ex: Manager: Will the project be finished at 3pm? Me: Later, I think. Boss: Could you finish it before the end of the day? Me: Yes, I can do that.

Is the word "party" implied in "barbecue"? and is it general to use this word (barbecue) like this?

Yes, it is implied that a barbecue (BBQ) is a type of social gathering or party. You do not need to add the word "party" after it, it can be used as is. Ex: My family is having a barbecue this weekend. Do you wanna come? Ex: Let's get together and have a barbecue.

What's the main difference between a "madam" and a "madame?"

The main difference is that "Madame" is a french title with the same respect as "Mrs." Whereas "madam" is a general polite term for a woman, although usually in authority or rank. "Ma'am" is also a common contracted form of "madam." Ex: Ma'am, can I leave class early, please? Ex: Madame Oceane is coming to visit today. Ex Madam Secretary, someone's here to see you.