こんにちは、ケビンさん。校正すること約束したんだから、今からそうしましょうね。
あるところ意味はよく分かっていると思いますが、その他にはまだ完全に分かっていない所もあります。その場合、二つの文章を書いておきました。可能性が二つという意味です。
それに日本語の意味も書いておきたのですね。
英語の勉強しながら、日本語も忘れないように説明を読んだらいいと思います。
それで、がっかりしないで。僕の意見ですが、誤りは恥ずかしいことじゃないから、習うチャンスですよ。例えば１４年間の勉強している僕もまだ誤りますよ。だから自身持っていきましょう。さ、行きましょうか？
よし、行きますよ。宜しくお願いします！

HI, Kevin!. I told you I would proofread so here we go. There are some parts I understand what you mean pretty well and there are some where I don't completely understand. So for those situtuations I included two sentences. That means that there are two possible sentences.
I thought that it would also be nice that while you are studying English you read the explanations in Japanese. So, don't be dissapointed if you make mistakes. It's just my opinion but mistakes aren't embarassing, they are opportunites to learn. For example, I have been studying Japanes for 14 years and I still make mistakes. SO, let's be confident in yourself! So, let's start! Are you ready?
Alright!

題名：How terrible of my English writing...

How terrible of my English writing, correct me please.
*I would like to know how terrible my English writing is. Please correct my errors.

この題名を日本語でいうと、

「僕の英語の書くことがどう下手か知りたいんですから、誤りを直してください。」

第一の文章：You need to open your heart...

You need to open your heart when you want to make some friends in this world.
*You need to open your heart if you want to make friends in this world.
OR
*If you want to make friends in this world you need to open your heart

ケビンさんの書いたような文章は正しいですが、文節を並べ直しても大体同じなニュアンスが表しています。
The way you wrote the sentence is correct but the same sense can be expressed if you rearrange the clauses.

日本語でいうと：
「この世界では友達を作りたいなら心が人に寛容出来なければなりません。」

第二の文章：Beginning of this year, I...

Beginning of this year, I started to make friend with others who live in Tokyo, I give a goal to myself what is like one week on person.
*At the beginning of this year, I started making friends with people living in Tokyo. I gave myself a limit of something like one person per week.

日本語の場合なら：
「今年の明け、東京に住んでいる他人と友達を作ってみかったんで、一週間で一人の友達のできる限りを決めました。」

第三の文章：Sometimes...sometimes not
Sometimes I can finished my goal and sometimes not.
*Soemtimes I was able to complete my goal and sometimes I wasn't.

「ときどき目標は出来ましたけど、ときどきそう出来ませんでした。」

第四の文章： From March, I started to use Italki...
From March, I started to use Italki try to speak with others in English.
*Since March, I have been using Italki to speak with others in English.
「３月から、ITALKIで他人と英語の話すことができました。」

第五の文章：There are so many...
There are so many amazing people in this website and is easy to found a partner.
*There are so many amazing people here and it's so easy to find a language partner.
「このサイトではたくさんな優しい人がいるから、言語の相手を探すのは簡単です。」

第六の文章： Recently, I got a advise…
Recently, I got a advise from my friend who also using Italki that I can write some essay and upload
*I got some advice recently from a fellow Italki friend that I should upload an essay to this site.
「最近、ITALKIの友達が僕に論文をこのサイトでもし上げた方がいいというアドバイスをくれました。」

第七の文章：The people will correct my essay so...
The people will correct my essay so I try do it from today.
*People are willing to correct my essay so today I am giving it a try.
「人が文章を直してくれますから、今日から書いてみようと思います。」

第八の文章：And, I started to write...
And, I started to write a diary using FB from last month, until now, I was keeping to write diary about two months.
*Since last month I have been using Facebook and until now I was keeping a diary for almost two months.
「それに、先月からフェイスブックで日記を書いています。今までの実際の日記も書いていました。」
You probably shouldn't start a sentence with “and” because it needs to be attached to a clause mid-sentence. Instead of “and” I would suggest “what's more” or you can just simply omit it all together.

第九の文章：I have no idea...
I have no idea about my writing skill had been improved or not.
But I feel confidence when I cheek my diary list.

*I have no idea how skilled I am at writing or whether it has improved but I feel confident checking my diary.

「僕の英語での書くことが得意かどうか、よくなったかどうか知れませんけど、日記をチェックすることのは自身を持っています。」

最後の文章：I hope this will be helpful for my English skill.
*I hope this will help me improve my English skills.
「この日記を書いて、英語の能力がよくなるといいと思います。」