I'd be happy to take a look at your essay. We'll see what we can do to proof those little mistakes we all make and to make the idioms flow smoothly. Line by line:
"Great Opportunities are some things that don't come very often."
A couple of things here. You don't need to capitalize "Opportunities," and the word "some" is unnecessary.
"When I was growing up in Oakland, California, with my younger brother only to support me in school, my life was hellish."
It should be "only my younger brother to support me . . . "
"Burglaries, rape, and murder were common things in my neighborhood with 3 murders coming around a 3 block radius of where I lived."
Put a comma after "neighborhood," and spell out "three." Change "coming around" to "occurring in."
"All I could think of during that violent period was to get out as soon as possible as I feared extremely for the well-being of my life and my family."
This would sound better if you changed the order of the sentence; maybe something like, "I felt extreme fear for my family and myself, and all I could think of was to get out as soon as possible." You don't really need to state that it was a violent period, since you've already made that point.
"After seeing a group of men fleeing away from my house, which I later found out that it had been burglarized, I knew I had to get into college at all costs and someday stabilize my neighborhood."
Take out "that it." I would also add "return to" between "someday" and "stabilize."
"Living with fear in my neighborhood was an unfortunate circumstance and with my parents low salary it was impossible to gain a college education."
Insert a comma after "circumstance," and put an apostrophe after parents, since it's a possessive.
"College was my opportunity of a one-way ticket out of my bad neighborhood."
Change "opportunity of" to "opportunity for." Also, I'd eliminate "one-way," since you've indicated that you want to come back some day to make reforms (which is a truly inspiring idea, by the way!)
"My mother and father worked low-paying jobs only to support me into going to school."
Take out "only" and change "into going to" to "through."
"During the communist era in China, my mother and father were lucky enough to attend school."
Take out "enough."
"My mother was lucky enough to go through a few more grades then my father."
Change "then" to "than."
"I had trouble in math and English in high-school because neither of my parents was well educated in the fields of math and English."
"Well-educated" needs a hyphen. Change "in the fields of math and English" to "those fields."
"My parents still have limited English since they have been here for about 20 years."
Insert a comma after "English," and change "since" to "even though."
"She told me stories about how $1 could buy a week full of groceries because she didn't make much when she first immigrated."
I think what you're trying to say here is that your mother only had one dollar a week to spend on groceries. Be sure to spell out "one dollar."
"It became apparent that my parents didn't know how to do math when I showed them my 3rd grade homework which included multiplication and division problems."
You need a comma after "homework."
"Every night, I would go over the materials that were learned the next day in order to learn what the teacher was lecturing about."
Replace "were learned" with "for."
"Being accepted to a University of California will be one of the many great accomplishments I will ever fulfill."
It might be better to end this sentence with ". . . accomplishments I hope to achieve."
And the rest is fine--except you need a final period on the last sentence.
It sounds like you have great ambitions, and I wish you the best. You have obviously put a lot of thought into your essay, and your English is really very good. I hope my suggestions for some small changes will help you express yourself in "just right" idiomatic English.