First notebook entry: Introducing myself.

I'm teacher at a University and I teach chemical engineering. I want to learn English becasue I want to study PhD in another country. My mother tongue is Persian and I was born in Iran.

Althought the way you wrote is not incorrect but there are other better ways to frame it. For instance:

My name is Omid and I was born in Iran. My mother tounge is Persian and I teach chemical engineering at a university. I want to learn English because I want to study PhD in another country.

First notebook entry: Introducing myself, I live in Iran and I'm teacher in University.

I am learning English, becasue I want to studies Phd section in other country.
My mother's tongue is Persion. and I will help to anyone whom would like to learn Presion.