Can surgery fix a torn meniscus?

Depends. Yes, but many factors affect the success of meniscus repair. These include age of the patient (better if younger than 40), location of the tear, and the type of tear. Your surgeon will likely take all these points into consideration when performing your surgery.
Yes. Depending on the exact nature of the tear the meniscus may heal on it's own. If surgery is needed, the meniscus may be "cleaned up" to promote healing or repaired if there is a structural issue and the blood supply is sufficient.