Is there national/ethnic discrimination against Asians in U.S. graduate school admissions and in university faculty hiring
There is quite a bit of academic research on university entry and race, mostly in US universities, so if you are interested in learning about racial discrimination in academia, this would be a good place to start.  The phenomenon of discrimination against Asians in academia is well-known and has been identified regularly over the past twenty to thirty years, both in academic literature (e.g., Tsuang 1989, Wu 1995, Wong and Halgin 2011, Kim et al 2011) and in the press (see e.g., The Economist 2015).  The Asian-American Coalition for Education claim that there is widespread discrimination against Asians in academia, particularly in the elite Ivy-league schools, and they provide references to a number of articles and books discussing this issue.

This issue has been studied in quite a bit of detail by the economist Thomas Sowell in the context of his research on affirmative action (an overview of his ideas on the subject is here and his recent book on the economics and politics of race is here).  Sowell argues that affirmative action leads to discrimination against Asian applicants, as a consequence of this group having a higher proportion of applicants with high grades/skills.  Since Asians are the "model minority", Sowell argues that the use of affirmative action in academia tends to involve a raising of the bar for entry for this group, in order to try to avoid their "overrepresentation".

Anyway, this is a big subject, and a lot has been written on it.  Some users on this site may be able to give their own anecdotal experiences, but I recommend you examine this broader literature.  The links I have provided will get you started, but there is also plenty more on the topic.

UPDATE: There is presently a major lawsuit against Harvard University for alleged discrimination against Asian applicants.  It is alleged that Harvard admission staff have systematically down-rated Asian applicants on their "personality" in order to achieve racial balancing, consistent with the university's goal of racial diversity.  @BlueRoses: If this is a topic that interests you, I cannot think of a better example than for you to watch how this legal case plays out.