Something about me

The younger son of a business family, I was born in 1993 and raised in China’s coastal province Fujian.

I am the younger son of a business family , borned in 1993 and raised in a coastal province ,  Fujian , in China.

Youngest or eldest or 2nd or 3rd son.  Younger?? How many are there?

in a China’s coastal province ,Fujian. > Sounds not so smooth.

My ( limitless) /passion for knowledge were ignited by my father, a businessman who has devoted his whole life to the/our family firm.

Limitless > too strong a word( my opinion coz it sounds exaggerated)) . Passion > strong emotion of liking/interest something , likely for a long time.

My passion is collecting stamps .

enthusiasms> strong emotion of interest ,but may be over before you know it .

Passion is more enduring and enthusiasm is more momentarily felt.

A family firm > Which one ?' The /Our firm' points to your firm.

In his generation, the access to education was politically blocked thus many people in my hometown travelled across border to find their silver linings by setting up small businesses.

In his generation , (the ) access to education was politically hindered , thus many people in my hometown had to travel elsewhere to find a better life by setting up small businesses.

Because it was difficult to get education , they HAD to ...or must travel to > sounds more correct.

Blocked means none can get . Hindered > made difficult to get.

A silver lining is an metaphor . Be more precise unless you want to sound like that ) I wont, not in this context. No need for 'big words" if a simple understood word carries the same and better meaning.

Across border? What border > Of country ? Of provinces? Across the border of our province..ok

Even when  many have become successful entrepreneurs later, my father keeps telling me that rags-to-riches stories could not be written in the old way.????

Rags-to-rches stories from yesteryears are no longer an option to follow now.

As an advocate of knowledge, he gives me unfettered attentions and believes that it is an age of intellectual.

As an advocate of knowledge , he gives me a lot of encouragements to acquire knowledge as he believes this is the age of the intellectual.

unfettered > not controlled/ not retricted>see this > http://www.vocabulary.com/dictionary/unfettered.

unfettered attentions> correct word ,but from your construction , encouragement is better , I think.

My dad give me his unfettered attentions on my studies/He pays much attention on my studies

Even the skepticism and incomprehension for of my persistence in my pursuance of a higher education never stop from my other families, I still remember my father’s teaching and always push myself to get ahead in study.

Even when the skepticism and incomprehension expressed by other families for my persistance in pursuing a higher education never seem to stop/cease , I would still remember my father's words and always strive to get ahead/ do well in my studies .