내년의 난 대학의 졸업할 거야. = Next year I will graduate from college.

=> Another way: Your sentence is okay and this is another way of saying it.

Next year I'm going to graduate from college.​

그들은 나무에 자기 이름을 새겼다. = They carved their names on the tree.✔​

​​=> Corrected : The sentence is corrected grammatically.​

susan은 미술관에서 전시할 예정이야. = Susan is going to exhibit at the art museum.✔

​=> Corrected : The sentence is corrected grammatically.

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Thank you, Eunchan~