Does "grown-up" generally mean "adult" in most of the situation? Or does he use "grown-up" as a joking manner here?

What's the main difference between a "hat" and a "helmet?"

The difference between a "hat" and a "helmet" is that a helmet is made specifically for protection. People such as police officers, sportsmen, soldiers, and more where a helmet for protection. Whereas a "hat" doesn't have as much padding and is used for style or just protection from the sun. Ex: If you're going to ride your bike, you need to get your helmet. Ex: I need a hat to complete this outfit.

What's "govern" mean here?

"To govern" means to lead or control the actions of a state, organization, or people. Ex: President Yoon governs the people of Korea. Ex: The principal doesn't know how to govern the school. The students are out of control.

What does "fine for" mean?

"Fines" is plural for "fine", which in this context means a fee someone pays as a punishment, such as not returning a library book on time or breaking the law. "For" in this sentence is a conjunction between "fines" and "all the books", meaning the fine was due because the books were late.

What does "smoldering" mean, and what are the other expressions that can be replaced?

"Smoldering" refers to something burning slowly where there is smoke but no flame. Therefore, like in this context, "smoldering" is slang for describing someone as being attractive, as though they are "hot". In this context, "smoldering" could be replaced by "dashing". Ex: Did you see him? He has dashing good looks.

What does “break your heart” mean?

To "break someone's heart" means to cause them to feel extremely sad or sorrowful about something. Ex: He broke her heart when he left her for another girl. Ex: It breaks my heart to see so many stray dogs without homes.