Problems of Korean Education system are summarized to in two points. First, the primary education system from elementary school to high school are is uniform and doesn't reflect diversity. To enter the university, anyone  everyone should take  a test and the result of  the test decides (-S) which univ. he can enter. Although one is can be especially good at in some areas, he can't get the  a good result if  he does not study all subjects.

The second problem is the private education that takes requires a high cost. Most students go to the academy and their parents suffer from the burden.

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First, the primary education system from elementary school to high school areuniform and doesn't reflect diversity.

--If a sentence becomes too long and you cannot determine the conjugation of the verb, minus details from the sentence.

--> First, the primary education system from elementary school to high school are uniform and doesn't reflect diversity.
--This is how we know it should be changed to "the primary education system.....is"
--Notice you had "doesn't" which is conjugated correctly. So you must have noticed it's singular.

Lastly, good job on the compound nouns + he (If somebody commits a crime, he should be punished)!