Here are the corrections for the underlined parts:

1. Do you know about Sue? She's **given up** her job. (Correct)
2. My mother has **grown** up in Scotland. → My mother **grew** up in Scotland.
3. How many plays has Shakespeare **written**? (Correct)
4. Ow! I've **cut** my finger. It's bleeding. (Correct)
5. Drugs **have become** a big problem everywhere. (Correct)
6. The Chinese **have invented** paper. (Correct)
7. Where **have you been born**? → Where **were you born**?
8. Mary isn't at home. She's **gone** shopping. (Correct)
9. Albert Einstein **has been** the scientist who **developed** the theory of relativity. → Albert Einstein **was** the scientist who **developed** the theory of relativity.

Let me know if you need any more help!