[part2: A Family Member]

Describe someone in your family who you like.
Outline:
-How this person is related to you
-What this person looks like
-What kind of person he/she is
-Why you like this person


I love all my family members, but I would like to talk about my mother
because I am especially close to her.

She is of average height and weight, and has short black curly hair and bright sparkling eyes. Most people say she has clean skin and looks young for her age.

["clean skin" is nt really an English expression. We would often say someone has "young looking skin" or "smooth skin"]

She is passionate to learn new things. She enrolled into University when she was over 50 years old and now she is a student in a graduate school. She is also very outgoing and open minded so she dosen’t hesitate to make a new friends with foreigners or young people.

One of the things I love about her is her sense of humor. so iIt’s always fun to talk to her.
My mom is my best friend., and wWe share our problems or secrets and help each other.

**Excellent - very hard to find any problems with this piece of writing. Like I commented above I would probably change "clean skin" to "smooth skin", otherwise it suggests that your mum has lots of baths! I think you mean to say that she looks young?

Also, the last sentence finishes quickly to my ear. There is nothing wrong with it, but it would be more natural something like this: "We share our problems or secrets and help each other with our problems."****

[part2: A Family Member]

Describe someone in your family who you like.
Outline:
-How this person is related to you
-What this person looks like
-What kind of person he/she is
-Why you like this person


I love all my family members, but I would like to talk about my mother
because I am especially close to her.

She is of average height and weight, and has short, black curly hair and bright sparkling eyes. Most people say she has clean skin and looks young for her age.

She is passionate to learn new things. She enrolled into a university when she was over 50 years old and now she is a student in a graduate school. She is also very outgoing and open minded, so she dosen’t hesitate to make a new friend with foreigners or young people.

One of the things I love about her is her sense of humor, so it’s always fun to talk to her.
My mom is my best friend. and We share our problems or secrets and help each other.

General Notes:

--Very well written! Mostly minor punctuation mistakes here and there. 

--You say she has 'black' hair, but the following statement doesn't mention the color of her eyes. If you are expressing characteristics of the body in this way, it is best to also state the eye color if you are already stating the hair color. Although, culturally, this may not have the same significance. 

--"enrolled into university..." is probably a debatable subject, depending on the culture speaking English specificaly. With regards to American English, the only generic qualifier is 'college' to describe entering any program for earning a degree. A university is instead a 'place' rather than encompassing the program itself. Alternatively, you could use the name of the university here ("enrolled into [Name] University..."). University only being capitalized if it is part of a name.

--"...she is a student in graduate school." Might be better written as "...she is a graduate student." Unless you are referencing something else, where you might say "...she is attending graduate school."

--In your final statement, there are too many instances of 'and'. You can easily separate with a period (.) to establish additional statements like I have corrected.