Black thumbnails saying Ewr-access or .evocache folder read/write error! Check filesystem permissions.

That message means b2evolution cannot create or access the thumbnail image file or a directory to store it in. b2evolution tries to create hidden directories named .evocache or _evocache to store the thumbnails. Make sure all sub-directories of the /media folder are writable by PHP.

This often happens after moving or restoring media files and folders via FTP. You have media files and folders in place but they do not have write permissions for PHP.

Read more about Directory and File Permissions and Media File Permission Errors. You may request help from your hosting provider to achieve this. Ask your tech support "How do I make all files and folders within my /media directory to be writable by PHP?".

Black thumbnails saying Emime image/png

That message means "Error Mime type not supported: image/png". b2evolution cannot yet generate thumbnails for PNG images. We are working on it.

Why are the thumbnail error messages so short and so cryptic?

Because the thumbnails can potentially be very small and we need to have as much information as possible in the very first characters, since the rest may be cropped off.