안녕하세요. Lucia입니다.
National Merit Scholarship은 제가 진행을 따로 해본적은 없습니다.
특히나 미국 시민권자에게만 주는 장학금인데, 자녀분께서 시민권자이신지요?
https://www.nationalmerit.org/s/1758/interior.aspx?sid=1758&gid=2&pgid=424
Student Entry Requirements
To participate in the National Merit® Scholarship Program, a student must:
take the PSAT/NMSQT® in the specified year of the high school program and no later than the third year in grades 9 through 12,
regardless of grade classification or educational pattern;
be enrolled as a high school student (traditional or homeschooled), progressing normally toward graduation or completion of high school,
and planning to accept admission to college no later than the fall following completion of high school; and
be a citizen of the United States; or be a U.S. lawful permanent resident (or have applied for permanent residence, the application for which has not been denied)
and intend to become a U.S. citizen at the earliest opportunity allowed by law.
Not yet a U.S. citizen? Click here for documentation required from scholarship candidates who have not yet become U.S. citizens. (Adobe Acrobat Reader is required.)
The student's responses to items on the PSAT/NMSQT answer sheet that are specific to NMSC program entry determine
whether the individual meets requirements to participate in the National Merit Scholarship Program. Click here to see NMSC program entry items on the PSAT/NMSQT answer sheet.
Score reports provided for test takers and their schools indicate whether the student meets program entry requirements.
A school official or the student should report immediately to NMSC any error or change in reported information that may affect participation.
https://www.nationalmerit.org/s/1758/interior.aspx?sid=1758&gid=2&pgid=398
Students who meet published program entry and participation requirements* enter the National Merit® Scholarship Program by taking the Preliminary SAT/National 
Merit Scholarship Qualifying Test (PSAT/NMSQT®) at the specified time in the high school program, usually as juniors. Each year's PSAT/NMSQT is the qualifying test designated for entry to a particular year's competition. For example, the 2017 PSAT/NMSQT is the qualifying test for entry to the competition for scholarships to be awarded in 2019.
Registration for the test is by high school rather than individual student. Interested students should see their counselor at the beginning of the school year to make arrangements to take the PSAT/NMSQT at the school in the fall.
Note: The PSAT 10 and PSAT 8/9 will not be considered for entry to the National Merit Scholarship Program. The PSAT/NMSQT is the official route of entry to the National Merit Scholarship Program.
* To review the entry and participation requirements, go to the National Merit Scholarship Program page.
따라서, 개별적으로 재단에 신청하는 제도가 아니라, 학교 선생님께 학기가 시작하기 전에 Request를 해야 별도로 따로 진행할 수 있을 것으로 생각됩니다.
전체적으로 학생이 미국 대학 입시를 위한 준비를 잘 하고 있습니다.
GPA도 좋고, Test 성적도 좋고, (PSAT 성적이 고득점이지만, 실전 SAT와는 상당한 Gap이 있으니,
긴장의 끈을 놓지말고 열심히 준비하라고 해주십시오.) activity도 좋습니다.
다만, 공부하고자 하는 전공이 어떤 것인지 그것에 관련한 좀더 세부적인 activity가 더 있으면 좋겠네요.
이과쪽을 준비하는 학생이라면, Science Fair같은 것을 준비하여, Research paper같은 것을 대학 입시때 제출해도 좋구요.
추천서도 어떤 분께 부탁드릴 것인지 잘 생각해두는 것이 좋을 듯 합니다.
장학금에 관련해서는 학교 선생님과 상의하시는 것이 좋겠습니다.
