I would love if the system could somehow have the same permission sharing pop that appears in GMail when sharing Google Drive content to remind you something may not be shared.

Indeed.. because we can't see folders, we have to search for exact file names.

Please allow folder to show in search results.. not so we can try to attach them, but so we can double-click on them to see the files inside.

As for the other part of the OP's request, I've created a request for the attachment of actual files

Definitely agree for for the ability to add Drive files as attachments instead of links, and the ability to store directly to drive.

Also being able to store attachments from a given email directly into G-Drive!