First notebook entry: Introducing myself

I am a native Chinese speaker and I am currently a PhD student.

To add onto the comment made by Kat, we typically do not begin a sentence with "and." In some cases though, it is okay to start the sentence with an "And." However, in your example, you would not, and I think you should combine the first and second sentences because they are both short and related (talking about who who you are).

I want to find someone (with whom: formal) to practice my oral English (with: colloquial) and I will help you with your Chinese.

"With whom" would make your sentence a little bit more formal. You could tack on "with" to the end of your sentence instead, if you wanted to be more colloquial or informal. If you were writing a research paper, you would not want to end the sentece with "with," as you will commonly hear that you should not end your sentences with a preposition (with, on, at, over, etc.).

First notebook entry: Introducing myself

I am a native Chinese speaker. I am currently a PhD student. I want to find someone to practice my oral English and I will help you with your Chinese.

Just a small note, we do not typically start a sentence with the word "and'. Other than that good entry.