Hello, Saulo! I hope this helps!

Learning English (Titles are capitalized)

I started learning English by myself seriously about one year ago. (If you put the word "seriously" in front of the word "learning", it would sound more natural) During this year, I improved a lot in writing, grammar, and reading, but,(No comma necessary here) not always was with ease (Or you could say, "...but it was not always easy."). And, of course, I keep making mistakes. (If you're talking about the past, it needs to say, "I kept making mistakes." If you're talking about the present time, this sentence is correct.)

My listening was terrible at that moment time ("Moment" sounds more like something that happened in one instance, not over a gradual period of time). I tried so many times to watch movies on tv or listen to music and comprehend them the words, but, I was not able to (Technically, in English writing, we do not end words with prepositions, such as "to". In English speaking, we do it all the time. It depends on what you want to do).
I thought I had achieved (Or, "reached") my limit.
I was almost giving had almost given up, when I found some archives online with courses made especially made to for beginners. That was my breakthrough. I was listening everyday every day, everywhere, and every during all my freetime.
About a month ago, I downloaded an Android app called Stitcher, which gives (You could also say, "...which provides.") us an enormous amount of podcasts to practice your listening to English skills. I usually listen to it every day. Now, I can watch movies and series without subtitles, and I can understand the main ideas, even though,(No comma necessary here) I don't understand every single word. I have seen how much daily English practice in all areas can help us improve our skills.

Now, it's time to for one more breakthrough. I'm taking lessons with professional teachers on Italki. I prepared an a daily schedule to enhance all my English skills. I'll follow it, and soon I hope I'll be able to speak to friends from all over the world without writing one word. (I think you mean without having to type a word on Skype or something so they can understand you, but you might need to make that more clear here)

Today was the day to train my writing, so, that's it. I'll come back next week.

Beforehand, thank you all for the corrections.

Good luck, Saulo! I hope you achieve all your English-speaking goals, and that one day you will be able to speak naturally and fluently!