Sure, here are the transformed sentences:

7. I just want a mechanic to service my car. (HAVE)
→ I would prefer **to have my car serviced** by a mechanic.

8. Rumours are that this castle is David Beckham's. (BELONG)
→ This castle **is rumoured to belong** to David Beckham.

9. The class enthusiastically discussed where to go on their school trip. (DISCUSSION)
→ It was with **enthusiastic discussion that** they might go on their school trip.

10. Apart from John, everyone else plays tennis much worse than Helen. (NOWHERE)
→ With the **exception of John, everyone else is nowhere near as good as Helen at playing tennis.**