Something to read

I would hereby like to express my interest in the ASF program and to provide peace volunteer service in Poland. There are several reasons why I find it attractive to doing volunteer service, especially in Poland.

Wow... I did some work with them many years ago - good to hear ASF is still going!

I'm not exactly sure what peace volunteer service means. The confusing part is peace.  Should it be in another form, or do you mean Peace Corps?

Your last sentence was a little too formal - remember you're talking about yourself now!

Firstly, I won’t doubt I would have many problems in communicating with local people during my volunteer service, as I have been studying Polish language at the Kyiv-Mohyla Academy for nearly two years now, and understand it at quite a good level. Furthermore, I had read many books in Polish to write my profound academic Bachelor thesis. Now, I continue to read Polish online newspapers, such as “Gazeta Wyborća”, “Magazyn Historyćny” and so on. Therefore, my knowledge of Polish is a big challenge considerable ability that allows me to handle a variety of tasks effectively and to convey information accurately and concisely.

Basically, I've fixed the tenses and made adjustments to make it clearer.

Secondly, it would be a great opportunity for me to learn more about Poland as a country. I would like to tell you that I began to take interests in Polish history and culture about four years ago. During that time I realized that Ukraine and Poland have a lot of similarities. For example, these two countries were both a part of the Rzeczpospolita (the Polish–Lithuanian Commonwealth). They both suffered from the terror of National Socialism and were occupied by the Soviet Union. However, now Poland and Ukraine are developing in different ways. Thus, it would be useful for me to break past old stereotypes as well as better understand Polish society.

Thirdly, I wish to understand how Polish NGOs, government organizations and businesses work. It would allows me to compare Ukrainian and Polish models of management, communications and so on. This new knowledge will be helpful in my future professional career.

I'm curious - what is your future professional career?  It may be helpful to mention it.

Last but not least, I would have the opportunity to attend several Polish cultural events, such as theatre, literary or music festivals. Last summer in Kyiv I had the fortune of seeing a performance by one Polish street theatre troupe and was very inspired by their work because of the show. So I desire to know more about live Polish culture.

To answer the question about my hopes and fears, I would like to emphasize that I expect to gain relevant work experience from working in such a friendly atmosphere. I also expect that my living conditions would be sufficient to my modest needs and that I would enjoy time to relax at the weekend. On the other hand, I am aware that some difficulties may arise during my volunteer service and that sometimes I may have to do lots a certain amount of routine work. So I am preparing myself to solve everyday problems and learn something new if it will be necessary.

The constant use of will makes you sound very demanding and pushy.  Use would for a softer and more polite tone.

Apart form that, good luck with your application! Where in Poland do you expect to go? I'm only familiar with Krakow.