Here are the corrections for the underlined words:

1. **me** → **to**
- Corrected: My parents let me stay out late.

2. **talk** → **to talk**
- Corrected: You're not allowed to talk during the exam.

3. **allow** → **allowed**
- Corrected: I'm not allowed to have friends round tomorrow.

4. **don’t** → **doesn't**
- Corrected: My friend doesn't let me use his skateboard.

5. **saw** → **seen**
- Corrected: If I had seen you, I would have said hi.

6. **would have** → **had**
- Corrected: If you had come, you would have had fun.

These corrections ensure proper grammar and structure.