Here are the rewritten sentences using "Would/Do you mind + If..." and "Would you mind + Ving":

1. Can I move the refrigerator?
→ **Would you mind if I moved the refrigerator?**

2. Could I sit here?
→ **Do you mind if I sit here?**

3. May I ask you a question?
→ **Would you mind if I asked you a question?**
Could I turn the radio on?
→ **Do you mind turning the radio on?**

4. Could I borrow your dictionary?
→ **Would you mind if I borrowed your dictionary?**

5. Can you take me a photograph?
→ **Would you mind taking a photograph of me?**

6. Could you wait for a moment?
→ **Would you mind waiting for a moment?**
Will you post this letter for me?
→ **Would you mind posting this letter for me?**

7. Can I turn on the TV?
→ **Would you mind if I turned on the TV?**

8. Can you correct the composition for me?
→ **Do you mind correcting the composition for me?**

9. Can I take a photo of you?
→ **Would you mind if I took a photo of you?**

10. Can I give some advice about your study habit?
→ **Do you mind if I give some advice about your study habit?**

11. Can you play the tape one more time?
→ **Would you mind playing the tape one more time?**

12. Can I borrow your dictionary?
→ **Do you mind if I borrow your dictionary?**

13. Could you tell me how to learn English at school?
→ **Would you mind telling me how to learn English at school?**

14. Could I have a look at your homework?
→ **Would you mind if I had a look at your homework?**