1. Between the two different paths, i am still debating which one works the best for me. but before i have to decide what to do in my life, i guess i need to first figure out which one to put in the career goal essay. any suggestion?
First goal is way too vague. Working for a "big corporation" in general management is not going to demonstrate that you are ready to make the MBA move right now. The second goal is more in alignment with your first goal but frankly makes the most sense if you do a part time instead of a full time MBA program. It is not too common to rejoin your current employer. They would likely see through this.
2. For both of the goals, are they too general or vague? should I add more details? Yes.
3. If i decided to pick the entrepreneurship, is it a good idea to mention my connections in china such as the entrepreneur in the real estate? Also, for the long term goal, do i need to specify i would like to focus in which fields or industry? Or it is ok to say something general? since the long term goal doesn't require as much detail as the short term one?
The more focused you are the better in general. B-schools like to know that you have been around the block enough to know what you want and have laid the foundation to get there in your experience thus far. The MBA should be a catalyst, but not the whole formula to achieving your goals. It's great to mention the connections in China, as they are an important part of the thread which is connecting your experience to your future.
4. also about the entrepreneurship, does my short-term goal and long-term goal make sense together?
I am unclear on your long term goal #2--if your goal is to move this same business to China, then yes, the two goals make sense together. Expanding internationally would be a valid goal. If you are talking about starting over with some new kind of business in China down the road, it seems there is not a very good connection.
5. many of the entrepreneurship concentration also focus on innovation, for example the entrepreneurship and innovation concentration in Johnson. For such concentration, does the school expect the candidates have both entrepreneurship and technology background? for someone like me, who has some experience of working in a start-up business and like to continue entrepreneurship in retail, is that an disadvantage for me if i want to go with one of those "entrepreneurship & innovation" concentration?
Yes in a certain sense your entrepreneurial vision for retail will not be as exciting or "fundable" from a b-school or VC perspective. You will also likely not find classmates who will want to join you in such a venture, which could work against you.
6. I remember reading one of the article talks about "DNAs of the top MBA programs". If i decide to go with my entrepreneurship career goal, does it go well with "DNAs"of Johnson, Darden, Stern, and Sloan?
Definitely not Johnson, STern or Sloan. Mabye Darden or McCombs. do some due dilligence on what companies came out of those schools and see where your vision fits in.