Is 던 better or 한?

Which of the two sentences would be correct?

1. 하던 일을 마저 해 치우자.
2. 한 일을 마저 해 치우자.

Sentence 1 is the correct sentence.

하던 일을 마저 해 치우자.
Let's finish the work we were doing.

Sentence 1 is correct because 던 can imply that the work was interrupted, whereas 한 implies that the work was completed, leaving nothing to finish.

Now let's consider the opposite situation. Which of the following two sentences would be correct?

1. 여기가 내가 졸업하던 학교다.
2. 여기가 내가 졸업한 학교다.
   

Sentence 2 is correct.

여기가 내가 졸업한 학교다.
This is the school I graduated from.

Sentence 2 is correct because the verb 졸업하다 means you "have completed your studies," so 한 is more appropriate here than 하던.