This is possible, when you click the header in the table of contents you'll see a string starting with heading appended to the URL like so:
Share out the URL with the #heading string at the end and when users open the doc it will open directly to that heading.
YouTube does not support this kind of thing, you need to specify which email addresses exactly should have access.
As a workaround, you can record a screen capture of you performing the steps to reproduce yourself and upload those as a public video.
By default sharing a folder in Google Drive (in your case "Big Folder") - any file or folder inside it (in your case "Small Folder") is shared with the same people.
Therefore, if you have not changed settings, everything you move from "Big Folder" to "Small Folder" will be shared the same. And no one will lose access.
But if you have changed the sharing ...
From a comment by Maxim:
Currently (2016.08), if I share a folder with another person, all files inside this folder get shared as well, but not the subfolders. In other words, Google Docs sharing it is not recursive, indeed, (though not in the way @Fibonacci described this).