Here are the mistakes in each sentence:

1. "Don't write on my mum **book.**"
**Mistake:** Should be "Don't write in my mum's book."

2. "Don't take the blue hat. It's Ms. **Lan** hat."
**Mistake:** Should be "It's Ms. Lan's hat."

3. "My dad brother is a doctor."
**Mistake:** Should be "My dad **is** a doctor." (or "My **brother** is a doctor.")

4. "**Nam** dog is lying under the table."
**Mistake:** Should be "My dog is lying under the table." (if "Nam" refers to a dog, it should be "Nam's dog.")

5. "My parents **room** is next to my room."
**Mistake:** Should be "My parents' room is next to my room."

Feel free to ask if you have more questions!