Would it change the nuance of the statement if I say "can" or "may" instead of "might"? I thought either "may" or "can" refer to a possibility of something!

What does "wintergreen" mean?

"Wintergreen" is the flavor of breath mints she is talking about. "Wintergreens" are a family of plants which have a minty flavor, so it is a common flavor used for breath mints and gum.

Can you tell me some alternative words that can replace "hey"?

"Hey" is used as an exclamation here. To have the same effect, you can also use "oh," "by the way," or "oi" here. Ex: Oh, what's he doing? = Oi, what's he doing?

Is "hang in there" often used? What does it mean?

"Hang in there" is an informal expression that is often used as a form of encouragement to not give up, even in difficult times or circumstances. The speaker has used this expression to state that he is still persisting on and not doing too poorly. Ex: Exam season is almost over. Hang in there! Ex: It's been a rough year. But I'm still hanging in there.

What does "am about to" mean?

When you are "about to do" something, you are going to do it very soon. It means that something will happen or be done soon. Ex: I'm about to leave. Are you ready to go? Ex: Are you about to go somewhere? Can I go with you?

Is "give that to" here used as the same meaning as "owing to"?

Yes, to "give to" in this context means to give someone the credit for doing something which is similar to "owing to", however it is more about giving someone recognition than actually owing them something. This is not a very common use of the phrase "give to". Ex: I give it all to her, she's done most of the work. Ex: He gave me all the credit for coming up with the idea.