I have a small question. Usually in survival analysis, the event is something bad, e.g death, relapse of a disease, etc...Now what if I have data in which the event is positive, e.g., time to healing, where of course healing is defined properly. Can I use the same methods of survival analysis (KM, log rank, cox,...), or is there any difference ? What about the censoring mechanism ?
No reason not to do this. You'll often see time to response as an outcome in clinical trials. You can also have outcomes which are somewhat more neutral, e.g., treatment duration.
Censoring is the same, but you should consider whether censoring is actually uninformative (a requirement for KM, Cox) - if not you should use competing risks framework (same goes for negative outcomes).