Happiness

I am learning English because I want to work in countries where English is spoken.

My native language is Portuguese and I grew up in Brazil.

I enjoy going out with my friends and family and traveling around my country and abroad.

When you say 'enjoy' and you are refering to activities, you always end the verbs in 'ing.' For example, I enjoy reading.  Also, the commas are not necessary so I deleted them.

Introducing myself

I am learning English because I want to talk with my friends in the U.S. My native language is Vietnamese and i grew up in Vietnam. I enjoy playing tennis and listening to music.  (Just like how you had the verb play end in ing in that sentence, listen is going to end in ing as well)

Capitalization rules: Always capitalize the first letter in a sentence, always capitalize the name of a language or a country and always capitalize a name.

Audio Tracks

I love reading notebooks on italki, and Someone corrects it (The 's' is not capitalized because you don't have a specific name). I can learn a lot of knowledges (This is implied and not necessary because you are talking about learning) from corrections. It is useful to learn a language, but I have a poor pronounciation (pronounce is the verb and the noun is pronunciation). I cann't speak it well. Audio tracks are the best way to learn a language(I cleaned up those last two sentences to make them clearer).  When I am free, I can hear them again and again. This will increase our interest in learning a language. (You don't want to put a possessive because its not clear who 'our' is.  You can leave it blank)

Wish you all have a great future in the New Year.

(Good work)

First notebook entry: Introducing myself

HI
I am learning English, because I want to study abroad/work in Perú and make friends from Perú. My native language is Spanish and I grew up in Spain.
I enjoy playing the guitar and learning medicine.

(The names of languages are always capitalized just like countries.  You needed an and between clauses, just like in your second sentence.  When you talk about enjoying something, it ends in 'ing'.  For example, "I enjoy reading.")

YY English Corner

Yesterday, I signed(You have to use past tense here) in the YY English Corner,(space after comma) it was my first time to use my cell phone and attend an English Corner at home. It was a very unique way.

In this English Corner, each person has to download YY software first, and after you have signed in, you type some key words (I would take out the 'can' here just because you are giving guidelines) which can help you find an "English Corner". Then, after you access (the word choice is strange) the "room", you wait for the opportunity to speak, called "Pai Mai".  (two spaces here)After that, if there is an opportunity for you, you choose a topic (took out another can and a would in the next line) and chat with the host. Other listeners send you a flower if your spoken English is fluent or your topic is interesting.

Yesterday, I was so nervous, so some people, who heard my voice, typed that they thought I was thirsty. but they all liked my film gossip.  (This sentence is confusing without commas. Also, we don't usually used typed.  Most people use 'said' even though it was typed)

(It looks like this is just tense issues mostly.  Since you are describing the room and giving instructions in second person, it involves different dense use.  You can technically leave in the can but it looks awkward to a native English speaker.  Great job though, this is a complicated well-written paragraph)

Hello,everyone!

Hello,(space here after the comma) everyone! These days, I get (Use the present if you are still recieving it.  Also, most people would say get instead of recieve but that's just word choice) a lot from italki and by skype, I have (Use perfect) made some friends like Chris, Ande (captialize names), and others (Most people would just say others because you already said that they were friends).  (Two spaces at the end of a sentence)Now I'm grateful to italki for all of these.
I love English and I hope that more people can become my language partner and we can study together.
Thank you for reading. (Most people would just say this)
My SKYPE name :Shao Johnson.

If you remember the space after the comma and two spaces after the period, you are well on your way.  Most of your errors here are just mastering how people talk and not the language.  There are two tense errors based on what time period you are talking about, but great job.