I think any ghost can randomly appear walking in neighborhoods under certain circumstances: Spooky Day, Ghost Night at a bar.
Releasing the ghost to the netherworld will delete the ghost sim completely.
Your ghost is playable in part because the urn/tombstone is on your home lot, so if you carried the urn/tombstone in a sim's personal inventory to a non-residential lot instead, and put it there, your ghost would no longer be playable. I don't offhand know the easiest way to do that though-- whether you'd split the ghost off from the main family in Household Manager first, or what.