The format is fine in my opinion. There is no rule that everything has to be 3 paragraphs long, that is just a simple format taught to novice essay writers to help them create a basic essay. A paragraph can be a single sentence if appropriate. The main thing to avoid is letting paragraphs get too long, and it is good style to vary the length of the paragraphs. All short or all long paragraphs is poor style.
You make some good points but have some errors. I've made some corrections for you in blue in the first paragraph and have highlighted other areas you need to work on in red.
I have studied the International Relations at (name of university) university from 2003 to 2007 and acquired a bachelor degree. During four years of university-life, I was imparted with plenty of political knowledge, including Diplomacy, International Low ('Low' not understandable), Human Rights and International Organizations. However, I was tremendously interested in researches related to Eastern Mentality and Democracy. During my studies I have been faced with a broad range of fundamental problems with which contemporary societies, and in particular the post-Soviet countries, are confronted. My marks have been 'good' and 'excellent'. I got them in a country where corruption is widely spread and where 80 % students prefer get their degrees by their connections or money. But I am proud of my university grades because they are result of my hard work. and which might be diminished but obliviously were not exaggerated. I also did get average marks at my former primary school but in entrance test examinations I got high points and was accepted to one of the most competitive faculties of one of the prestigious University in ***. (Thus I exceed lots of classmates who got formal excellent grades. By the way it was one more prove of non objective evaluation. I'd drop this part as it just sounds like complaining.)
As nowadays corruption and lack of democracy are the headache of our society, it is of vital importance to me to gain analytical and comprehensible insight into these processes in order to deal with the fundamental problems of our global world is facing.
Being deeply interested in issues related to democracy, and European integration, I took a high number of courses on European and American studies. These subjects taught me that the Western System is a very special entity with a promising prospect for my country, but in which a lot of work still needs to be done. With this vision your master would offer me an excellent opportunity to increase my knowledge with regard to the International Relations.
The international aspects of my current studies reflect my great interest and curiosity in global education and foreign languages. Seven years living in Ukraine and one year in Russia, provided me with an indispensable cultural experience. Additionally, my internship at The Ministry of Foreign Affairs and work experiences in the different NGO provided me with professional work experience in the field of International Relations and Human Rights Issues. Both experiences show that I am able to express myself in other languages and easily adapt to new situations. Moreover, I know how to deal with cultural differences due to the multicultural environment at my University. My open personality creates an outgoing person with strong interpersonal skills. Personally, I am a person with a high perseverance level, someone who is motivated and ambitious. My teachers know me as a courteous and resourceful student and my classmates know me as a light-hearted friend and an enthusiasm coworker.
Studying abroad is a big challenge in a number of respects. It will put me into a new cultural and studying environment. It will help me to be more mature, to have better social skills and to be more flexible in my thinking. It will make very big impact on my growth as an independent thinking person thus will make me more necessary in my own country which has great demand on democratic thinking people. On this program I will have the chance to broaden my cultural awareness and to contribute to my flexibility and creativity. Studying and living in a different culture will help me to see the world from a completely different perspective.
I do hope that by my above-motivation words, I will be accepted as an applicant and a beneficiary of the US University. I understand that admission to the University of *** is competitive, but I also understand that I’m qualified, eager and prepared to meet all of the challenges I will be presented with. I, therefore, would be most grateful if you could give my application form in your most favorable consideration. I hope you will give me the privilege of continuing my studies at your fine institution. I'm looking forward to hearing from you.