3. My mother often says, "When the time comes, you'll know." / My mother often says that when the time comes, we'll know.
=> Why not "if" instead of "when"
7. " Last night, I was sleeping soundly when I was suddenly awakened," she said. / She said that last night she was sleeping soundly when she was suddenly awakened.
=> Why the same tense?
8. "We shall let you know the answer next month," the manager told us.
The manager told us that they should let us know the answer the following month.
=> Why not 'would'? Use 'should' for advice.
9. " Most poisonous snakes run away when they see people, " he told them. / He told them that most poisonous snakes ran away when they saw people.
=> 'run away...see'. It's a general truth so keep the tense. :D
10. I shall tell him, "You have no proof. " / I shall tell him that he has no proof.
=> What about? You said you would tell him that he had no proof.