Indirect speech

I would really like to know if these sentences are correct:

  1. She said that she was waiting for Ann.
  2. I asked where my books were.
  3. He said that he liked reading novels written in English.
  4. Our teacher said that he had read our compositions 2 days before.
  5. The workers said that they would go on strike the next day.
  6. He said that he had celebrated his birthday the month before.
  7. I didn’t believe that that very well-known singer had been /was addicted to drugs for many years and that she would commit suicide.
    8.He said that the teacher had to answer the students’ questions.
  8. He said that he had seen the film the day before.
  9. She believed that a pet could help an withdrawn child be sociable and friendly.
    Thank you for your time and support!


They seem all right except for (10) - She believed that a pet could help a withdrawn child (to) become (this would be better than ‘be’) sociable and friendly.


Thank you a lot, Alan! What about sentence nr. 7? Are both tenses acceptable?In sentence nr. 10 we have the article ‘a’ because ‘withdrawn’ begins with a consonant?