My recent career

I graduated from Hannam University with a background (I would use the word degree over background) in Convention Hotel Management.

Before graduatied graduating from university, I had took taken a year off and I worked at Lotte Hotel at that time the English idiom "for the time being" sounds better here although you could rearrange this sentence in many ways for it to make sense.

Soon afterward after, managers and captains was turnig were beginning to like me, because I worked really hard, and I could learn so much about the service industry. I'm a bit confused about what you were trying to convey, but I think you simply meant that since you worked very hard, you could learn a lot about the service industry. If that's the case, then I would recommend turning that sentence into its own personal sentence since it's not exactly related to the other two sentences and the sentence may become a run on sentence if that makes sense.

However, I had dicided decided to study English, so I quit my job and took a lesson lessons from at the SDA English Institute in Seoul.

I studied English at the institue for 7 months and came went back to university.

Prior to graduate gaduation, one of my professor had recommended a job in at a hotel for me, and I had interviews at the hotel. Instead I would say "..., and I went to a series of interviews at the hotel"

They offered to me a job, but I really wanted to come to the United States to study more, so I declined and came to America to study English more instead. For this sentence, I would rewrite it a bit because it was almost becoming repetitive and a run on sentence. Personally I would write "The hotel offered me a job, but I declined their offer. I really wanted to travel to the United  States to study more before taking a job there." or something along that line. Your sentences weren't really wrong, I just think it sounds more natural that way.

After I finish my courses here, I will travel around the America and then go back to my country. I will find my a job in there as soon as posiible possible.

Your English is really good and I enjoyed reading about your interesting career path up to this point. I also find it amazing that you're doing all of this to learn English. You're awesome, and I hope I helped a little!