Hi! I'm not a native English speaker but I think i can help :) i've copied your text and written in capital letters the mistakes.
Peoples' Friendship University in Moscow.
In this university, you can learn more than one language.
Personally, I'm interested in the Faculty of Journalism.
TO become a student of the faculty is very difficult (AS) IT requires a high knowledge of the Russian language and literature. It is also necessary to write an essay and pass the test.
THE faculty of Journalism has modern equipmentS and competent lecturers.
Students can have an internship abroad (YOU TYPED A FULL STOP HERE WHICH IS INCORRECT) to study with people from other countries. This is a wonderful experience when you learn the language and can speak with a native speaker.
The university is popular in Russia. But its graduates have throughout the world.
I can't really understand what you mean in the last sentence but this is what I would write:
THE UNIVERSITY IS POPULAR IN RUSSIA, BUT ITS GRADUATES HAVE GONE THROUGHOUT THE WORLD.
But I'm not 100% sure of my version ;)
Hope that helps!