What is my hobby?..... Um,  I think my hobby is studying.  I am not a very intelligent person, but I want to understand the principle of the world and the law of nature. I also desire to become a wise person. But I do not practice my hobby constantly, because my mood is unstable.  My another hobby is playing the piano. I like classical music, because it gives me deep and rich inspiration. I can't play the piano often, either.  I'm not so good at playing the piano because I don't have enough time to do it. But I hope to play the piano very well some day. My third favorite hobby is listening to the radio. It connects the world and me. I usually listen to the radio while washing the dishes or cooking food or sewing the clothes. The good point of the radio is that I can do other things at the same time. Nowadays I enjoy listening to MBC FM channel. The programs of this channel is easy, interesting, and full of very useful information. 

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Correction:     Student's sentence        Corrected sentence        Grammar explanation       Better sentence   

What is my hobby?..... Um,  I think my hobby is studying. 

What is my hobby? I think my hobby is studying. 

You can erase "..... Um,", It's not necessary for the sentence. 

I am not a very intelligent person, but I want to understand the principle of the world and the law of nature. 

I am not an intelligent person, but I want to understand the principle of the world and the law of nature. 

"Very" is not necessary for the sentence.

But I do not practice my hobby constantly, because my mood is unstable.

This sentence is correct. 

My another hobby is playing the piano. I like classical music, because it gives me deep and rich inspiration.

My other hobby is playing the piano. I like classical music because it gives me deep and rich inspiration.

Change the word "another" to "other". Erase comma (,) after music because it's not necessary. 

I can't play the piano often, either. 

This sentence is correct. 

I'm not so good at playing the piano because I don't have enough time to do it. But I hope to play the piano very well some day.

I'm not so good at playing the piano because I don't have enough time to do it. But I hope to play the piano very well someday.  

"Someday" doesn't have a space in between of "some" and "day".

My third favorite hobby is listening to the radio. It connects the world and me. I usually listen to the radio while washing the dishes or cooking food or sewing the clothes.

My third favorite hobby is listening to the radio. It connects the world and me. I usually listen to the radio while washing the dishes or cooking food or sewing clothes.

"The" is not necessary for the sentence.

The good point of the radio is that I can do other things at the same time.

This sentence is correct. 

Nowadays I enjoy listening to MBC FM channel. The programs of this channel is easy, interesting, and full of very useful information. 

Nowadays I enjoy listening to the MBC FM channel. The programs of this channel are easy, interesting, and full of very useful information. 

Add the article "the" before MBC. Change "is" to "are" because you are talking about the programs in the channel.