correst these sentences!

1. Mary is not only my classmate, but also my best friend.

2. She is always around me and help me to solve various problems.

3. She likes to point out my mistakes.

4. I really feel discourage sometimes, but I think she just want me to improve.

5. She is my angel as my life becomes more beautiful and colorful.
OR
5. She is my angel as my living becomes more beautiful and colorful.

6. (Your current sentence has no meaning because there is no VERB)
I think I cannot live/survive without him.

7. Unfortunately, Mary died yesterday.
OR
7. Unfortunately, Mary passed away yesterday.
(Personally, I would use "passed away" when talking about someone else's death as this is a more formal!)

8. Actually, I am really sad.
OR
8. Actually, I am very sad.
(Both "really" and "very" is OK, the only mistake is that you can't use both at the same time!)

9. She is an important person in my life.

10. I think I cannot forget her.
OR
10. I think I will never forget her. (This sounds more natural English!)

11. We must cherish our precious friendship.
OR
11. We should cherish our precious friendship.
(It's OK to use "must" if it's a written sentence, if it's conversation then use "should" Moreover, by saying "precious friendship" it already have the meaning of "friends", so, there is no need to repeat the word "our friends" in the 1st part!)

12. Hong Kong is a stressful city.

13. Everyone seems to be under a lot of stress/pressure at work or at school.

14. So, we need friends to release our stress as they share our happiness or sadness.
OR
14. So, we need friends to be there to share our happiness and sadness in order to release our stress.
(The 2nd sentence will sounds more natural than the 1st one!)

Some of the sentence I have more than one version. This is due to the fact that I cannot get a clear meaning from your original sentence because of the grammatical errors, which by changing these errors could change the meaning of the sentence. Anyway, hope these will help! :)

1.Mary not only is my classmate, but also my best friend.

2.She is always around me and helps me to solve different problems.

3.She likes to point out my mistakes.

4.I sometime really feel sorrowful , but I think she just want me to improve.

5.She is my angel as my live become beautiful and colorful.

6.I think I cannot (?) without him. <---survive? live?

7.Unfortunately, Mary was dead yesterday.

8.Actually, I am really very sad.

9.She is an important person in my whole life.

10.I think I cannot forget her forever.

11.We must always cherish our friends and our precious friendship.

12.Hong Kong is a stressful city.

13.Everyone seems to be under a lot of pressure at work or at school.

14.So we need friends to release our pressure since they share our happiness and sadness.

1. Mary is not only my classmate but also my best friend .

2. She always goes around with me and helps me to solve different problems .

3.She likes to point out my mistakes.

4.I really feel sorrowful sometimes, but I think she just want me can improve.

5.She is my angel as my life become beautiful and colorful.

6.I think I cannot without him.

7.Unfortunately, Mary died yesterday.

8.Actually, I am really sad.

9.She is important in my life.

10.I think I never can forget her .

11.We must cherish our precious friendship.

12.Hong Kong is a tressful city.

13.Everyone seems to be under a lot of pressure at work or at school.

14.So we need friends to release our pressure that they share our happiness or sadness.