Scans/jobs not moving
Background jobs are driven by the WordPress scheduler. On very low-traffic sites the queue may need a nudge — keeping the image list open is enough (the plugin's status updates keep the queue moving). Under Jobs & Logs you see the queue in real time.
Images marked as failed
Filter by Failed in the image list. Open Jobs & Logs and expand "Technical details" on the error row — it shows the cause (e.g. missing file or memory limit). Select the images and run the bulk action Re-run failed action once the cause is fixed.
"Nothing to do" when compressing
It means the image is already compressed harder than the chosen quality — recompression would have made the file larger, so the plugin declined. Try a lower quality if you still want to shrink it.
The diagnostics report
Under Settings → Advanced there is a ready-made report with server info, library stats and capabilities. Click "Copy diagnostics report" and paste it into your support ticket — it speeds up help considerably.