Here are the correct answers for the questions:

13. A. because
14. C. take
15. D. the biggest
16. A. bigger
17. B. role
18. A. mustn’t
19. C. will be
20. D. What do you think

For the rearranging conversation answers:
a) Don't be silly, you'll do great!
b) Absolutely. You know your stuff inside and out.
c) I’m a little worried about the upcoming presentation.
d) Thanks, that actually makes me feel a bit better.
e) Really? Do you think so?

For correcting a mistake in each sentence, the sentence that requires correction is:

"Nick is thinking about where he will be tomorrow. He doesn’t want to stay at home." (The verb "thinking" should be in the present continuous form, so it should remain correct).

Other sentences seem grammatically correct; however, if there are specific mistakes you want checked, let me know!