In answer to your last question, no, there’s no way for all folders to be shared with other users by default. To get nearly the same result, it easy enough to create shared folders; anything created within those folders will also be shared.
The simplest way to do this is using the Group Folders app. You’ll need to create a group and add your users to it, then you can create as many shared folders as you want for all members of the group. Users can still create files or folders outside of the shared folders, which will be private by default.
You can disable sharing between users, so that nobody can create and share their own ad-hoc shares - they’ll have to use the centralized folder, or ask you to create a new one as appropriate.