1. Who wrote this letter? Who is this letter for?

Bora wrote this letter. This letter is for Ms. Kim.

Bora wrote this letter to Ms. Kim her teacher from last year.

(Are the two answers correct?)

2. Bora's school begins at 8:30 a.m.
My school begins at 8:30 a.m. as well.
However, my school is over at 3:10 p.m.
She goes to a drama club, but I go to
a sports club. I also miss my old teachers' classes.

(Is this passage grammatical? Would you check the errors? Thank you.)

1. Who wrote this letter? Who is this letter for?

Bora wrote this letter. This letter is for Ms. Kim.

Bora wrote this letter to Ms. Kim her teacher from last year.

(Are the two answers correct?)
All looks correct except that you need to add a comma after "Ms. Kim" in the last sentence.

2. Bora's school begins at 8:30 a.m.
My school begins at 8:30 a.m. as well.
However, my school is over at 3:10 p.m.
She goes to a drama club, but I go to
a sports club. I also miss my old teachers' classes.

(Is this passage grammatical? Would you check the errors? Thank you.)
All looks good here, too. The only suggestion I'd make regards the word "old" -- do you really mean OLD?? Or do you mean "my former teachers' classes"?

1. Yes, the two answers provided are correct. Bora wrote the letter and it is addressed to Ms. Kim, her teacher from last year.

2. The passage is grammatically correct, but there are a few errors that can be improved:

- Bora's school begins at 8:30 a.m., and so does my school.
- However, while Bora's school ends at 3:10 p.m., mine ends at 3:10 p.m. as well.
- Bora goes to a drama club, but I go to a sports club instead.
- Additionally, I miss my old teachers' classes.

In the revised version, the sentence structure and word choice are corrected for clarity.