I think it's written perfectly fine and pretty standard for a WSJ article.

Where would you like to visit in the future?
I would like to visit <strike>in</strike> Korea. I have been studying Korean for two years. I have never been <strike>to</strike> there. I would like to eat a delicious Korean dish there.

If you want an answer to your question, I would love to visit Japan, particularly Kyoto.

Hi, I'm trying to make some sentences using the new vocabulary I learnt today.
If there are any grammar mistakes and/or weird word choices, please correct them. Thanks.

1)The falcon nibbles at some game.
(This is actually kind of difficult. I'm not sure if an animal thats hunted by other animals is considered "game". At least I've never heard it used in that context. I always thought of "game" as the animals humans hunted.)

2) A hawk soared into the sky.

3) A rustic dwelling is made from a bold structure.

4) The elaborate swivel chair has a hefty price.

5) This looks like a good spot to rustle up some rare delicacies.

6) I give the room a once over, the floor creaks slightly when I walk on it.

7) I shut my book and put it back on the self on the way out.

8) Sure enough, I should have filled in a phoney name at the front desk.

9) I startled by ringing the phone, I hung it up and shoved it back into my pocket.

10) I become a solitary explorer and try to acclimate myself to the new place.

なんか、複雑な例文ｗ。よく意味が分かりませんけど本当に面白い。

Overall, very excellently written. Your English is fantastic. I actually had to double check the definition of acclimate. You indeed used it correctly. I don't really hear it that much in everyday conversation but that's okay. Maybe a more natural way to phrase it would be "get used to" or "get accustomed". Good job.

My Shortcoming

While my colleagues often praise me as a loyal and faithful person, I often make careless mistakes and it is one of my shortcomings.

For instance, I've bought tickets with wrong destinations or dates many times so far. Whenever I make such mistakes, I vow never to make that mistake anymore. Nevertheless, I repeat similar mistakes again and again.

Traveling is one of my hobbies, but I frequently have trouble during travel while traveling due to my drawback I mentioned above. So, I really want to know how to reform this weak point.

Hello again, Yuko

Again, overall a really good job. However, as I had mentioned in my previous post, your writing style is a bit stiff. The underlined section, while nothing wrong grammatically, just sounds very unnatural and a native English speaker wouldn't say it like that. Maybe something like "So, I really want to work on this and improve my bad habits" or "So, I want to work on not making those mistakes" and so on. There is many different ways you could say it. Trying to sound more "natural" in a language you're learning is a really difficult skill, I know my Japanese writing can sound pretty strange sometimes. Really one of the only ways to improve on sounding more natural is just to be exposed to the language more. The only thing I can suggest is just to experience more native English material like reading books and watching television intended for native English speakers. If you ever have any questions feel free to message me :)

While my colleagues often praise me as a loyal and faithful person, I often make careless mistakes and it is one of my shortcomings.

For instance, I have bought tickets with wrong destinations or dates many times so far, though travel is one of my favorite things. Whenever I make such mistakes, I vow never to mistake anymore. Nevertheless, I repeat similar mistakes again and again. I want to know how to reform this weak point effectively.

Hello, Yuko

Overall, I think your English is excellent.If I had to critique something, it would probably be that your English sounds just a little bit stiff. Using "I've" instead of "I have" can help alleviate this. But that's just nitpicking, your English is great.
Also, the portion I underlined does sound a bit unsual since you were talking about your travel related mistakes and then just mention you like travelling. Just a little out of place. I hope you find this useful.

I have a good <strike>working</strike> <strike>companion</strike>(coworker/colleague).
Yesterday, we enjoyed eating pizza and pasta at a sports-bar, and we played table tennis.
Then we went to a karaoke (place/parlor) to sing songs.
It costs money, however it was a very happy time.
I thought that there might be sometimes such time.(Don't really understand this)

Today, I worked with my companion for four hours.
It is good approach to work with someone, because if I feel loneliness, my motivation for working is dropped. (this entire part sounds strange, not really sure what you're trying to say)
My plan <strike>after now </strike>later is to cook dinner and do the duties that were left.

I tried to edit this in a way that still retains the style you wrote it in, but making it sound natural and correcting grammer. 

Sounds good to me.