오늘은 너무 바빠요(present)/바빴어요(past).

   -"바쁘다" > "바빠요".

   -Using past tense is much natural in this situation! 

나는 음악을 가르쳐요/배워요. 음악 수업은 재미있었어요. 나는 학생들을 못알어요. 지금 너무 피곤해요!

  -Well, which sentence do you want to say, " I teach music" or "I learn music"?

  -If you want to say "I teach music", "나는 음악을 가르쳐요" is right sentence. If you want to say "I learn music", "나는 음악을 배워요." is right!

내일 아침에 한국어 수업이 있어요. 수업은 60분 이에요. (나는) 수업을 좋아해요.

  -"에" is similar meaning with "in". "은" is similar with "is". They are difficult, because that words are not in English.

  -Subject is missing. But without subject, people will understand.

 Very good job^^

I hope that the correction is helpful for you!