Cover Art images will be picked up if they are named correctly and in the correct location.
Episode Art must be in the same directory as the video file and be named the same, just with a different file extension.
Series and Season Cover Art images go in their respective sub-directories under the directory specified in "Options > File Location > Cover Art". The Series Cover Art is named the same as the [Series] field, while the Season Cover Art is named for the Series and Season. For example, "Lucifer - Season 2.jpg". Look in those sub-directories for examples.
It's all explained here:
https://wiki.jriver.com/index.php/Cover_ArtJRiver have no control over what is or isn't on TheTVDB site. So reporting it on the forum won't fix it, and MC is working correctly so there is nothing to fix there either.
If you have found the artwork you want to use through TMM, simply put it in the correct location and name it correctly.