I have set up a shared templates folder and I am able to move .scriv templates for whole projects to that folder to open.
Maybe I don’t follow what you mean here, but you would want to install project templates properly, as described in §5.4.5, Managing Templates, pg. 87.
The shared templates folder is an extension of the document template principle, not project templates. They are a way of having global files you can use to create new binder items within a project. For example I have one that inserts a bunch of lorem ipsum text. That’s useful to me no matter what project I’m using.
You can selectively add templates in either direction, as you please:
-
To bring a shared template into a specific project:
- Select the templates folder in that project.
- Use the
Project ▸ New From Template ▸submenu and select the shared template you wish to “fork” into this project.
-
To make a project’s template global, you need to create a file out of it:
- Select the template in the binder that you wish to make global.
- Use the
File ▸ Export ▸ Files...menu command, and target the shared template folder.
For best results you should leave most of the options disabled, so you don’t end up with metadata .txt files and so forth. Presumably you would want the main content file as a starting point alone.
I’d like to be able to, say, download a ‘project’ template someone made that has a ton of custom folders and ‘document’ templates and be able to pluck out a single ‘document’ template or a folder of templates from within the project itself and add them to this Shared Templates folder.
The above aside, another perfectly legitimate way of going about this is it open both projects at once, and drag any templates you want to gather from one binder to another. You can safely close and discard the other project you created, if that’s all you wanted from it.
I don’t see anywhere where the individual documents/folders of a project are saved apart from the whole ‘project’ .scriv file to be able to move them, and I cannot find an option for moving or selecting the folders or ‘document’ templates within an open project on Scrivener or to somehow recategorize them from there.
I’m not sure if I quite follow what you’re aiming for here, but having come from Windows, I take it you’re used to seeing the entire internal storage area of the project exposed as files and folders. One isn’t really meant to be messing that directly—that it is a folder at all is an unfortunately side effect of Windows not having the capability the Mac does, to essentially have folder-based “file formats”. The project was always meant to act as a single file.
These are referred as “packages” on a Mac, and by and large if something is a package you should leave it alone internally—certainly you wouldn’t want to use it as your own personal storage area. The main reason to go into these is to copy resources out, or make customisations—it’s more of power user thing. The Mac uses these for a lot of things; applications in fact are most often packages that you can go into and poke around. If you don’t like how a program’s default .css files work for instance, chances are you can “fix” them. Like I say, not something you’d want to do unless you know what you’re doing, though. 
But if you do need to for whatever reason, you would right-click on the package in Finder and select “Show Package Contents”.