I can understand your anxiety and frustration. But I think you will feel much better if you know how the American universities admit foreign students. You see there are many factors that are involved in the admission policy of a given university. In general, the universities use a quota system to sele ct foreign students. Each department makes its own policy as to how many foreign students it is going to admit each year. If there are too many Chinese students in the department, the department will be in favor of students from other countries. Moreover, the general economy and the fiscal conditions of the individual universities also play a key factor. Again, you are competing with other applicants. In other words, your success depends upon so many factors that are beyond your control. All you can do is present yourself in the best way you can.
A good letter of recommendation is helpful, but more important are your grades and scores of the required tests. Financial conditions can be important to some universities but normally are secondary consideration for most universities. There is however a strategy to consider when you are choosing a school.
Of course, you have a better chance in a less competitive institution, if you have a good standing academically. I know how difficult for you and your fellow students to know all the schools. I don't know myself either. So you spend more time researching the universities you are interested in and select the best that you like to apply. Forty some years ago, I went through the same agony of getting to this country forty as you are going through now. I hope that by knowing all the factors involved, you may feel less pressured.
Connections exist in every society. People do use influence and power to get what they want. But I must say that in the public universities here,equalcompetition rather than favoritism is the general rule. Private schools are a different story. Rich people can buy an
admission for their children. Many private schools charge high tuition and do accept foreign students who are less qualified academically.
I know how frustrated you feel when not getting a response for a letter you wrote to a professor. You see most professors are busy with their teaching and research. Even on campus students have hard time to catch them. So I am notsurprised that you don't hear from them. If they are interested in you, they will write you. I appreciate the pressure of uncertainties, which can be unbearable sometimes. But I do suggest that you be patient, hoping for the best.