Sharing content between Spaces

We have Pages relevant to several Spaces but not all — do we need to duplicate them?

No. The same Page can be made visible to multiple Teams.

If a post is shared to another Space and the original Space is deleted, does the post stay?

If you shared it using “Share to Space”, it becomes a separate post in the new Space and is not deleted, even if the original Space is. This is not the case when you use the “Reshare Post” function.