I'm sure you are learning advanced Korean.
We don't use "학교에 간 길이었어요"
I think you mean "학교에 가는 길이었어요."
"던" has meaning of past tense. "이었어요" is also past tense.
So first sentence is more correct. But we use second sentence often when I express or talk to others about my memories in realistic.
If that sentence is from movie, after 2nd sentence, scene might shift to the story about that way to the school.
Examp (2)
식당을 is right. not 이, because 식당 is object.
(B) and (c) is same, that means, now i'm looking for 식당 during this talk.
(A) means I was looking for 식당 just before you talk to me. (with eye contact with other person)
Are you clear?