Hi.  I kindly suggest these corrections. 

There is redundant use of the word the

2. One of our project members postulated his own strategy on how to deal with our management issue.

3. Mt. Fuji represents the most lofty mountain of Japan. 

If you would like to use representative,  it must pertain usually to a person.  So how about this sentence instead. 

Mr.  Steve Hopkins is our company's representative to the conference tomorrow. 

4. I enjoy seeing a myriad of stars every night.

5. The U.S. government stipulated the Japanese government to change its law after World War II.

6. Playing table tennis was proven to help people prevent Alzheimer's disease. 

Substantiated means to strengthen something most usually used for proof of evidence or arguments as in an investigation or a case trial or a statement made.

Her statements were substantiated by the evidence gathered by the police 

7. A question asks you to synthesize each claims between the passage and the lecture.

Thank you.

1. Both of the  presidential candidates have the huge number of partisans.

    - You are talking about a specific set of candidates.

2. One of our project members postulated his own strategy of how to deal with our management issue.

3. Mt. Fuji is the representative, lofty mountain of Japan

    - 'a' can work but I would say that Fuji  can be the 'definite article' because most only know of

    Mt. Fuji in relation to Japan,


4. I enjoy seeing a myriad of stars every night.

5. The U.S. government stipulated the Japanese government to change its laws after World War II.

    - I assume more than one law was changed?

6. Playing table tennis was tried to help people prevent Alzheimer's disease.

    - 'tried' makes more sense. 'substantiated' is usually used instead of 'justified'

7. A question asks you to synthesize each claims between the passage and the lecture.

    - Confused with what you are trying to say!

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