Gloria: My hobby is listen music and draw a picture
Correct: My hobbies  are listening to music and drawing pictures
Explanation: Singular means just one of the person, animal or thing which the noun refers to and you will use "is". Plural means more than one and you will use "are".

Gloria: I have my hobby in my rest time.
Correct:I do my hobby during my rest time/I  do my hobby during my free time.
Explanation: You could say either way above.

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Hi, Gloria!  Just like you, teacher likes to listen to music too. Anyway, thank you for submitting your homework. Great job, Gloria!

-Teacher Isabel