Moho's import feature should be fine; it doesn't appear to be doing anything wrong in this situation. If there's something wrong with the 'non-Moho' content, it needs to be fixed in another program (e.g., a compatible image, sound, or video editor). Sometimes, simply re-exporting or re-saving from the other program does the trick.
Using Moho's Library should be fine too, and if you're mainly using only Moho content on a small network, it can be a good system. I rarely use the feature myself, but mostly because I need to share data across multiple software packages and computers, which, in my opinion, exceeds the Library's capabilities.
Re: Importing old Moho files into a newer version, yes, this can have unexpected results because of the different data structures. The safest way to do this is to import or open the scene in the version of Moho you're using, test the rig, and make any necessary corrections. After the rig is working correctly, then it can be saved for that version of Moho, and imported into other projects of that same version.
The things to watch out for vary by Moho versions, rig structure, or workflow. For example, going backward from Moho 14 to an earlier version of Moho can add Bone Physics to all bones. In the past, I know moving files in or out of Moho 13.0 to other versions can cause all kinds of problems with Smart Bone Actions, so I avoid using 13.0 completely. Moho 13.5 (the Lost Marble version), on the other hand, is generally safe for import/export. Regardless, the rigs are always fixable if they show problems. After fixing them for a particular version of Moho, they should be fine for that version.
For example, the Mame-chan character, who appears in some of our tutorials, was originally created in Moho 13.0, then moved to Moho 12.5, and then moved to Moho 13.5, and finally brought into Moho 14.x when we started the tutorial series last year. I've had to make small adjustments and fixes in the rig for each Moho version, and it's since been fine to use in Moho 14.x all year long.