Ответ:

  1. When did you start learning French? — Two years ago, while I was preparing for my A levels.
  2. I didn’t know you had a dog. — I found her on the street a month ago while I was walking back from school.
  3. Julie passed all her exams. — Yes, I know. She told me the good news while we were having lunch.
  4. Did you clean the attic? — Yes, and I came across my yearbook.

Past Continuous обозначает длительное действие, на фоне которого произошло другое действие; Past Simple — завершённое действие в прошлом.