I moved to the US from Jordan when I was close to 5 years old, and had to speed-learn English in about a year. Should I mention that anywhere? Does it help me in the diversity factor?
You can mention it if you feel it is part of who you are. I don’t think it will help or hurt you in terms of college admissions.
Neutral.
There are lots of immigrant children. I don’t think it is a hook.
For the diversity factor, yes, they like people from everywhere, but they also want to attract the URM students: African American, Native American, Mexican-American, Pacific Islanders.
No difference.
It is so much easier for a 5 year old to learn a new language than it is for a 15 year old.
Haha you’ve all confirmed my thoughts on it. Thanks for the responses, all
i think a unique essay on that topic will help you, so maybe it will promote diversity
It depends how you look at it. In my opinion i think its a great advantage because colleges and schools look at uniqueness and your motivation. Being an immigrant, your first language may not be English and you may struggle to do good in your classes. If colleges see your motivation and discipline to excel in classes, then they will be excited about it. Also, It would make a great college essay. I come from an arabian immigrant family, many of the girls in my country get married at a young age (at age 12,13,14). No one in my family has ever went to college and i want to be the first to introduce education to my future family generation. You see… that is what my college essay will be about. Dont worry if youre afraid that youll be behind because youre an immigrant. Its all about hard work and motivation. 
Definitely mention that as a diversity factor! Columbia University, one of the top 7 ivy league colleges in the nation love diversity and i know people who were admitted because of there backstories!