Has anyone found a way to connect an external solid state drive with folders for each album content, with no music player software, to the Rossini to play?
Can Mosaic be used to control which tracks are being accessed?
Or do I need music player software like Audirvana?
Yes, to use Mosaic you need your files in storage e.g. NAS having a UPnP connection . dCS recommend and only support MinimServer 2 for UPnP. There will of course be music player software - this is what Mosaic is 
. Using e.g. a USB SSD will require a music player with UPnP such as JRiver MC.
You can plug a USB drive directly into some dCS components but this is not advised as things like artwork and random access are compromised. Use my earlier advice.
This will provide what you want.