(Who? You have to give the subject first.) He is famous musician in Korea. many Korean = Many Koreans say that he is genious.
because almost = Most of the / Most people think that his ablity of  = in composition is really awesome.
so he has received recognization = So he has been receiving recognitions as a singer from many people until now.
and so am i = I recognize his talent, too.
He has a lot of classic = classical music.
Among the classics, my favorite Korean song = most favorite is 다행이다. It is a mercy (what do oyu mean by mercy?) that  = which is sang by 이적.
The reason that  = why i like that song is good thing all around the melody is beautiful = is that the melody is timeless.
then, the song lyrics were pathetiacally touching. = Also, the lyrics of the song is very touching. (What do you mean by "pathetiacally touching"?)
so, to explain an overall story of that song, = The story of the song goes like this:
One man meets another one girl and date together all day, = a girl and they have a date the whole day.
and he wants to do all of things with her during his whole life. = He wants to do all the things and spend the rest of his life with her
For example, he wants to cook for her and touch her hair.
and hug her i = He also wants to hug her. I think he really wants her everthing.
so i do quiet nicely by my girl friend,  (what do you mean by this?) whenever i listen to it.