What you are calling the Main Library is also know in MC as the Default Library. It can't be moved and is always under the AppData directory. It can, however, be renamed to whatever you want. It also doesn't need to be the Library that you usually use. MC can be set to open the Default Library when it is started, and if it is not, it will open the previously open Library. So you can create a Library anywhere on your PC and have MC always open and use that Library, but MC will always also have a Default Library in the default location under AppData.
1)
If you back up a Library, the Library that you had loaded is backed up. None of the other Libraries are backed up or referenced in any way, other than they are listed in the settings, and therefore some information about them is stored in the Windows Registry. All libraries on a PC share the same settings, which are backed up with any Library, and Restored to the Registry when a Library Restore is done,if that option is selected.
So yes, you need to open and back up each library. MC will do automatic backups on a "regular" basis, but you can't control when that happens, so it isn't going to happen when you open each of your Libraries, say for the first time in a week. The automatic backups will happen only for the currently loaded Library, when MC thinks they are due to occur. Each Library backup ZIP file name includes the name of the Library by default, so you can tell which one they are for, even though they will all be stored in the same location, unless you manually change that location during a manual backup.
As above, the backups aren't 100% independent of each other, as they all back up and can be used to Restore a common set of settings. Otherwise, yes they are completely independent.
The Main Library, and all other Libraries on the one PC, should list all Libraries that have been created for that installation. This is required, as otherwise there isn't any way to switch Libraries. All information on what Libraries exist in the installation is stored in settings and is therefore visible in all Libraries.
2)
It works this way. Create Library A and back it up. Create Library B and back it up. Switch from Library A to B, then restore Library A. You will now have the same content in Library A and B. That is, you will have Library A under both Library names, A and B, but they will still be named A and B.
A Library Restore restores the library contents into the currently loaded Library, overwriting what was previously in that library. A Library Restore will not recreate a sub-directory structure based on where it was originally backed up from. It will load into the location of the currently loaded Library, and retain the name of the currently loaded Library.
If you backed up your Video Library, then deleted the location it used to be stored in (C:\JRMC_Libraries\Video\), then MC would have a problem, as it would think it had a Library in that location, but it couldn't find one. If you try to load the Library that you have deleted the sub-directory for, MC will re-create the original sub-directory for that Library, and create an empty Library "stub" consisting of six files, and then build more of the Library as required, when you start to use it.
In order to restore the Library again to its original location you would need to switch to that Library, then run the Restore. So if you deleted the sub-directory, switched to that Library again which re-created the sub-directory and a stub Library, then the Restore would overwrite that stub Library.
If you want to delete a Library permanently so that MC no longer knows about it, do it from within MC. But note that you cannot delete the Main/Default Library.
However, do you have a good reason for having multiple Libraries?
Most people use one Library, and then use MC's capabilities, specifically Views, to separate different types of content, as was intended and how MC is designed to be used. There are very few valid reasons for having multiple Libraries. I have just one real Library, and a few test Libraries on my Workstation, which is also a Client of my HTPC. My HTPC has just one Library, but includes all Audio, Video, Image, and Television media that my HTPC can access.
Some people have argued that they need multiple Libraries, but usually, their reasons aren't valid and are more often related to the way they have traditionally used Media software, or some personal preference, or some misunderstanding of how MC works.
If you had just one Library, none of the above issues would occur. A search of the forum will find multiple discussions about using multiple Libraries, rather than one with appropriate Views.