Would it sound awkward if I say "single" instead of "one" in this context?

What does "menacing" mean?

"Menacing" means dangerous, scary, or threatening! Ex: He had a menacing look on his face, so I backed away slowly. Ex: My neighbors own a menacing cat. It looks cute. But, It's not.

Is "she's" an abbreviation of "she has"?

Yes, "she's" means "she has" here.

There seems to be a few prepositions that can be used with "oneself". Could you explain the difference between "for oneself", "by oneself" and "in oneself"?

Here, "for oneself" means to do something on your own, rather than having someone else do it, and for one's own purpose or benefit. "By oneself" means without anyone else or alone. "In oneself" means something inside oneself, usually metaphorically. Ex: Find it in yourself to help him. => find the will, energy, or motivation Ex: I made dinner for myself last night. Ex: It feels like I did the group project by myself.

I heard that illegal aliens sometimes get deported outside the border. And let's assume their newborn babies automatically got citizenship. Then, what happens to those children if their parents are deported by authorities?

From what I know, in the US, the parents could be deported, but the children will probably be taken care of by the country's childcare services. They become a "ward of the state," placed under the care of a guardian or legal entity. In Ontario, children have the right to go to school and have an education, even if their parents are illegal immigrants.

What does "gravity centered" mean here? Is it an idiom?

"My gravity centered" here means "I am stable". "The center of gravity" is the point in an object or person where the wight of the object or person is equally distributed, so it is/they are "balanced" at that point. "Gravity centered" is specific to this song, not an idiom. Keep in mind that because this is art and a song, these lyrics are subject to different interpretations.