What does "let it go" mean?

Isn’t it right to say “she’s not good”?

"Not good" and "no good" are both grammatically correct, and can usually be used interchangeably. However, "no good" sometimes implies that something is worthless, useless, or in this case, dangerous. "Not good" may be less strong and implies that the word "good" does not apply to something, but it may not be completely worthless. You could use "she's not good" in this case if you wanted to, but "she's no good" is a little stronger.

What does "shut up" mean here? She didn't say a thing!

While the traditional meaning of "shut up" is to tell someone to be quiet. The meaning here is the informal usage to express disbelief, or even amazement. When this (politer) usage is intended, the phrase is uttered with mild inflexion to express surprise. So, here, Regina is surprised or amazed by the things Cady is telling her. Ex: Shut up! You won the top prize? Ex: Shut up! What are you doing here?

What does "hay" mean?

"Hay" is grass that has been cut and dried out, often used as feed for animals like horses. Ex: I lived on a farm, and we often just sat on the hay bales outside. Ex: Go and get the hay for the cattle.

Is "zoological garden" same as "zoo"? I think I have seen the word "zoological garden" in somewhere in Europe.

Yes, you are correct. "Zoo" is actually short for zoological garden. Sometimes, it is also called an animal park or menagerie. Ex: My favorite childhood memory is visiting the zoo with my family. Ex: With the onset of the pandemic, many zoos have implemented innovative ideas for social distancing, such as drive through tours and family sleepovers.

In what situation do you use the word "dear"? Are there any other meanings of "dear"?

The word "dear" has quite a few uses. It is often used to refer to a person who is really loved or liked by someone else. Ex: She was a very dear friend. Ex: He was very dear to me. "Dear" can also be used at the beginning of a letter or email to greet the person you are writing to. Usually this is a more formal way to start a letter or email. Ex: Dear Mum and Dad/Ms. Lewis. The way that "dear" is being used here is to express. We can use "dear" to show anger, disappointment, sadness, or surprise. Ex: Oh dear! I've lost my keys again. Ex: Dear me, it's already 4.30 and I told my mum I'd be home by 5.