My experience learning English

I studied English from middle school to the first year of my college, so I can say that I had studied English for more than seven years.

First, let me say that your English is amazing! So, I'm only making small corrections, for more advanced and native speakers.

Usually we just say "college" unless you are talking about the place specifically. See these two sentences:

"I studied English in college."
"At my college, there is a big library."

The reason is just saying "college" without "my" makes it more of a time of your life than a real place.

But under the pressure of English education in my country, learning English was an unpleasant experience for me.

English articles and prepositions are very very difficult and just take a lot of practice. Usually, it will be "for me" when you're talking about experiences or emotions. We use "to me" for physical actions like "He gave the pencil to me."

No matter what kind of subjects they want to study, schools require students to take an English proficiency examination such as the TOEIC or the TOEFL.

This is a native speaker thing, but with the names of tests, we add "the" before. It makes them sound scarier, I guess?

Especially the job market is very competetive, people study English desperately.

"Competitive" is when lots of people want something and only one person gets it.

"Compatible" is when two things or two people work well together. I think it was just a typing mistake ^_^

Studying English in Korea

You probably studied "gerunds" in school, so I won't explain too much. It's when you make a verb (action) into a noun (object). If you say "My hobby is studying English" or "I like watching movies" it's the same thing.

The reason we do it here, is because you're talking about a time in your life. So you could say it means "(The time of) studying English in Korea" Also, it's the topic of the next paragraph. So you could say it also means "(The topic of) studying English in Korea."

Shortly after graduating from my college, I signed in to a very famous English institution to prepare TOEIC examination.

You sign in "to" something in English.

He asked us to memorize at least a hundred vocabulary words a day.

It's weird, in English we have the single word "vocabulary" meaning a list of words, but we don't have a small unit like "vocabularies"

For the words on you vocabulary list, we just call them "vocabulary words" if you want to talk about a number of them. (The test was on twenty vocabulary words)

If you're curious, "vocabularies" refers to many different lists of words. As in "Please learn the food, home, and color vocabularies in English"

English in the USA

The country is always "the USA" "the United States" or "America."

I didn’t have any chance to meet native English speakers in Korea, and most of my friends’ TOEIC grades were not higher than mine.

Just typing mistakes, I think.

S for the first time.

You do something "for the first time" in English.

"I had pizza for the first time yesterday."
"I listened to rap music for the first time."

I had never learned those sentences when I leaned English and I decided to stay longer in the USA and study English for communicative purpose.

One more note, you can also say "the US" if you want. I think most native speakers in America call it either "the US" or "America."

Studying English in USA

Same as "Studying English in Korea"

I went to ESL class at Wright State University in Ohio.

We go to classes "at" a school. Usually, if you do something at a place, you use "at"

I was not happy because I wanted practice English with native speakers, but my teacher was the only native English speaker.

"The only" means there was one person who was a native speaker

"Only native English speak" means that the teacher was nothing else but a Native Speaker. As in, they couldn't speak any other language, or weren't a good teacher.

It's the same as the next sentence "the worst student" which is correct.

I was the worst student in my class, but my English proficiency had improved faster than other classmates because I spent most of my time outside practicing English instead of doing homework in the library.

Same meaning as "I like watching movies" again.

I went to fast food restaurants to listen how Americans order foods and what expressions they used, I asked strangers for directions even though I knew how to get there, and I audited university lectures to listen to the real classroom English.

Most native speakers never say "foods." There are some times to use "foods" but its most common to say "food" by itself.