Do I have to worry about transmitting malware/virus to others?

The Quarantine process places the disabled malware files in a folder, which can be reviewed or deleted as desired. Malware is not exactly a virus, but is bothersome none the less. Regardless, Macs are still at the stage where viruses are not at all common ... or even existent. Although, recently in the news, there is talk about the "Silver Sparrow" virus which currently does not have a destructive payload. Malwarebytes for Mac should be able to detect this virus and remove it.

It would not be re-transmitted if quarantined, and certainly not, if deleted.