The EasySocial output you see is not handled by JReviews. That's probably the EasySocial content plugin and to change the order in which it appears you need to play with the order of the content plugins in the Joomla Plugins Manager. Click on the order heading, then drag & drop the plugins in a different order so EasySocial goes first, then JReviews.
The setting for the cover only controls whether users can select a photo as cover, so it doesn't modify listings that already have covers assigned. If you want to remove covers and logos from all existing listings, then you should disable all the cover, logo related settings and then do a mass database update to revert the existing cover and logos to gallery images. You can do that with this database query:
UPDATE #__jreviews_media SET photo_function = NULL WHERE media_function IN ('logo','cover');
Replace #__ with your database table prefix.