In general your letter is very well done! I am a native English speaker! Judging your letter it is pretty formal so I would make my speach in the letter a little more formal... If this letter isn't supposed to be formal then it is good as it is! At the beginning of the letter when you introduce yourself instead of writing "I'm John Baker from Vilnius Užupis Gimnasium in Lithuania" I would write "My name is John Baker and I am from Vilnius Užupis Gimnasium in Lithuania". You could put a "The" at the beginning of the "First Reason" sentence. If you begin your sentence with just a "First reason" it makes the sentence incomplete so the correct term would be "The first reason". In the same sentence you are speaking as if your are already part of the project (It seems that you are asking to join the project.) "The first reason why we would like to take part of your project is..." seems to be accurate. The first sentence in the secound paragraph the "We have" should be replaced with a "We've" would be more appropriate. In another sentence when you say "some kind of new adventure" it would be better to replace it with "some new kind of adventure." Later in your last paragraph in your question "How many students could arrive to your school? " It should be "How many students could I send to your school?" Or "How many of my student can visit your school?" The first one is more formal so I would chose that instead. Overall your english is excellent, there were no spelling errors, and there were no problems with any past tense or future tense. I wish you luck on your letter!!!

Dear Students, I'm John Baker from Vilnius Užupis Gymnasium in Lithuania. I've just found your advertisement on the Internet. My class would like to participate in your project "Our traditions". The first reason for wanting to take part in your project is that we have found lots of information about Lithuanian traditions. We think it would be great to share some ideas and to find out something new. We have already participated in projects called "World problems" and "Food for Africa" in Germany. However, it was a long time ago and we are waiting for some kind of new adventure. Also, I would like to ask you some questions. How many students could you accommodate at your school and when would you be able to receive them? We are waiting anxiously for your reply and we hope to you soon! Best wishes, John