I'm also not a native english speaker, so grammar is not my forte, but I hope I can help you!
I think studying abroad is not only the time for studying but also the chance for growing as a human being in foreign country
I think it would be better " I believe this experience not only will help with my studies, but will be an irreplaceable chance for personal growht"
I am so aggressive and like to challenge many things
I think "aggressive" has a negative feeling to it. You may want to replace it with "resolute" or "competitive". Also you may try " I like to challange myself with many different activities"
reconsider about not only the relationship but also my home country, Japan
" about" is not needed after " reconsider". Also I think you could reformulate this statement a little
My finally dream is establishing strong Japan-Korea friendship
I would use "goal" instead of dream
Throughout this study abroad, I want to study about Japan-Korea relationship and consider what I can do for the friendship.
This concusion feels a little abrupt. I think you should spend same more words to make it more powerful and blend it better with the rest.
I hope you find this useful!