What does "a.k.a" mean? Is it used a lot?

What does “given the circumstances” mean?

"Given the circumstances" means considering everything. It is added to the sentence to say that an action or decision was necessary when it normally would not be. Hermione tells Harry that since Ron is in a relationship and she couldn't ask him to the Christmas party, she has had to ask someone else. Ex: Given the circumstances, I've had to apply to a different university. Ex: I have had to start work at a grocery store given the circumstances of my finances.

"loveliest" looks unfamiliar to me. Can I just use "the most lovely" instead of "loveliest"?

In this case, the two superlatives "most lovely" and "loveliest" are both acceptable. You can use both here. Ex: Jane is the loveliest girl I've ever met. = Jane is the most lovely girl I've ever met.

Why is it "mattress store"? Is it because she says "lie down"?

Yes, she is making a joke by saying he should "work at a mattress store" because she is accusing him of "lying down". What she means by "lie down" is "submit to your boss". She is saying that he submits to his boss too easily.

How can I know which one to use, "individual" or "person"? Could you explain the difference between two? Can I say "depressed person" here?

To answer your question, "person" and "individual" have similar meanings and are typically used synonymously. You can use either one and be correct. To answer your last question, yes, you can say "depressed person." However, since she says "depressed individuals," you would have to say "people who are depressed" or "depressed people" instead of "depressed person." Ex: The car was purchased by an individual from Europe. = The car was purchased by a person from Europe. Ex: Could you help that individual over there? = Could you help that person over there?

What does “front and back” mean in this situation?

"Front and back" in this situation means the 18-page letter that Rachel wrote for Ross. He says that the letter had writing on both the front of each page and on the back of each page. In this scene, Ross is mad at Rachel for making him read that long letter at three in the morning.