Depends on the context, but pretty much "to work" in this case means "to be fine" or "to not matter".

I hope that another war between North Korea and South Korea won't break out! (Normally it would be "a war", but since this is war has already happened in the past and might happen again, it'd would be "another war".) 

Lately, the relationship between North Korea and South Korea has been increasingly intense. I really hope there won't be any wars breaking out down the road!

(I wanted to correct what Nancy wrote. What you wrote was right: it is "relationship...has been", not "relationship...have been", because it's only one singular relationship. "Lately" can have a comma after it or not, either way is correct. I put "really hope" instead of "do hope" or just "hope" because it seems like you want to emphasize that this is your sincere feelings, and it sounds most natural this way.)

(Btw, I find it interesting the difference in perspective between us or perhaps, our countries when it comes to the meaning of "Korea". When Americans say "Korea", we think "South Korea". Only when we mean "North Korea" do we say that specific direction of the country. But you seem to use "Korea" to mean "North Korea", and speak of South Korea with the specific direction. That's interesting!)

 Me, too. He's my bias.

 The one I used just to get started that's really good and I highly recommend is Japanese SurvivalPhrases. They do a good job at explaining each word and phrase, and it improved my pronunciation. But honestly, your best bet is to just search the itunes store yourself under "Japanese", because there's several and you might find one that you like better.

There's no A in incredible. So it's incredible/incredibly.

If you actually want to read proficiently, you'll need to learn both, as many words are either in hiragana or katakana. It's really not that hard, as they're mostly the same pronunciations and often have similar strokes. I recommend starting with hiragana.

Listening to the Radio

Today I began to jog again. And I especially<strike> I</strike> tried to listen an English education program through the radio <strike>air</strike>.
As long as I remember what I learned, which is this:

I hate to put you out, but would you loan me a meal card? I put it on my desk. (You can say "would you loan me" or "would you let me borrow") 
당신을 괴롭히고 싶지는 않지만 식사 카드 좀 빌려 주시겠어요? 책상위에 놓고 나왔어요.

While you are editing and submitting the letter, please do mine, too (I'm not really sure quite what this is saying. The grammar is not clear. This is my best guess.)
그 문서 내는 김에 내 것도 같이 내줘.

I found that he is quite emotional. -<font class="Apple-style-span">or-</font> Is(n't) he quite emotional?
그 남자 꽤 감정적이더라.

If I do this activity, will I have more skills in English?

I'm thinking that, if this is what it is teaching you word-for-word, then it is not the best study guide for English, because there are several grammatical errors. If it is helping you with learning more words, then great. But I'm a little worried that it's not teaching correct English grammar, so please keep that in mind.

Successful People

Nowadays I am studying English at Academy<font class="Apple-style-span" color="#FF0000">,</font> 
요즘 나는 학원에서 영어 공부를 합니다.

and we use a book whi <meta http-equiv="Content-Type" content="text/html;charset=UTF-8" /><img src="http://www.italki.com/fckeditor/editor/skins/default/images/toolbar.buttonarrow.gif" width="5" height="3" alt="" />ch is written by Brian Tracy.
그리고 브라이언 트레이시가 지은 책을 이용합니다.

The subject is about successful people like himself.
그 주제는 자기와 같은 성공한 사람들에 관한 것 입니다.

Successful people think about their future specifically. 

They imagine, <strike>that</strike> "What would I be doing if my life was perfect in five years?
How much money would I have in the bank if my life was perfect?
What kind of home or marriage would I have if my life was perfect?"

i believe this is the rule of success. And now I want to share it with you.

Only think about your future. Only think about where you're going.

If you are, your door will open and you will get the same result as the top 10% of people in the world.