Dropbox doesn't have a permission model that looks like that. In Dropbox, you can create a share link for a file or folder (which can then be used by anyone who has that URL to read the contents of the file or folder), or you can share a folder (which gives specific users access to that folder in their own Dropbox).
Currently, the API only supports share links. So you can get a link for a file and then send that link to people you want to grant (read-only) access to.
Re: Check if folder exists and collect shared folder
It doesn't currently offer the ability to create shared folders though, as Steve mentioned.
In any case, it's not currently possible to make Dropbox send an email about it for you via the API, but I'll be sure to pass this along as a feature request.
We love to learn from the educators who use Dropbox. Whether you teach kids, teens, adults or a combination of all three, we want to know what apps and integrations you use with Dropbox to help with teaching. Which of the ones below is your favorite, or most used tool?