What does “shine up” mean?

What's "hard" mean here? Doesn't "hard" mean "difficult?"

It can mean "difficult," you're right. But here, it means "intensely" or "diligently." To do something with a great deal of effort! Ex: I worked so hard at exercising this year, and I can see the results now. Ex: The kids work hard at school. Ex: You were focusing so hard that you didn't hear me call your name.

Can I skip "will" here? Does it still make a sense without it?

If you drop "will" here then it will change the meaning of the sentence a little. "Will" is used here to indicate future tense, and that they will never know her now or in the future. If you remove "will" here then it would not necessarily indicate or emphasize that someone will never know her, and it would just indicate that in the past they've never known her. However, it would be grammatically correct to say "you never know me" and drop will.

What's "give in" mean and when's it used?

To "give in" means to yield or surrender, to stop fighting or arguing. Here, she is saying that she stopped fighting or resisting. Ex: Don't give in when someone pressures you to do something you don't want. Ex: Okay, okay, I give in. Let's do what you want!

What does "Be in charge of " mean?

To "be in charge of" something or someone means to be managing or responsible for something or someone. We use this when we want to express that our position holds a lot of responsibility. Ex: I am in charge of my whole family as I'm the oldest. Ex: As the manager, I am in charge of the five people.

What does “daybreak” mean here?

"Daybreak" is the name of the morning show she is applying to work for. Some examples of American morning shows are "Good Morning America" and "the Today Show".