I now have a set of [/font].mp3 Sermon audio files for which I want to create another library on the same local SSD on my MBP, and be able to switch between the two 'on the fly' thru File>Library> Music Library (or) Sermon Library, as I have named them.
What you propose should work just fine with no "mixing" or "interference" between the libraries. Switching libraries should be easy, but might take 10 seconds or so for each library to load. The main disadvantages of what you propose are:
1. Slow switching between libraries. With views it's nearly instant.
2. Duplication of settings, views, and other common things between libraries. You'll have to manually update each one if you change a preference or setting, or column layout, etc in either library.
I would lean towards using one Library and using Views to separate Music from Sermons. But you can do it either way. It's your choice and MC can do both.
On to your questions:
1. Where does the Main Library belong, and will it take care of both media libraries?
It can go in any empty directory. I've listed the default path above several times. You can keep the Main library there for simplicity.
NO: It will not hold both Libraries. Each Library requires it's own separate directory. Understand that I am talking about the MC database, which is called a Library. NOT the media files. Media files can be anywhere, though you probably want them separated at the top level into "Sermons" and "Music".
2. Where do the individual Music and Sermon Libraries belong so there is no mixing or interference when I switch from one to another?
As I stated above, one way to do it is to establish a new top level directory for Libraries. For example:
<your user directory>/Documents/J River/Libraries/
So your sermons library would live in:
<your user directory>/Documents/J River/Libraries/sermons/
Setting up the Sermons Library is easy. Just add a new library with:
file > Library > Library Manager > add library > Local library > Path > browse > (go to the location listed above)
Getting your main library moved is not as easy. MC does not have a supported way of fully moving a library. You kind of need to create a clone or a fresh library, make sure it works, and then delete the original. I'm not going to go into detail because it requires so many steps. I don't want to confuse things. I would leave your main library right where it is for now, assuming it works correctly.
3. Where do the Library Backups for each Library belong?
Library backup location are set by this option:
Tools > Options > File Location > Program Files > Library Backups > (path here)
You can use the same path for all libraries if you want. Because MC will make backup ZIP files that have the name of the library and the date in the file name. So it's easy to know which one is which. Or you can put them in different locations if you want. Just set the option appropriately in each individual library. I would personally leave it set as is.
Brian.