Your comments
I agree the icons should be svg. I just haven't had time to convert them or find new ones.
I've added a filter in the next update. If you want to go ahead and add it to your version here are the steps.
Edit this file...
WP-Review-Slider-Pro\wp-review-slider-pro\public\partials\template_class.php
around line 761 before the return add this line...
$logo = apply_filters( 'wprevpro_modify_sourcelogo', $logo, $review, $currentform );

Then in your theme functions.php file you can use it like so...
add_filter( 'wprevpro_modify_sourcelogo' , 'modify_sourcelogo', 10, 4 );
function modify_sourcelogo($logo, $review, $currentform) {
if($review->type=="Google" ){
$newlogo = '
';
}
return $newlogo;
}

The number either comes from the Review List downloaded count or the Source Page count. The values should get updated whenever you download new reviews. Which badge style are you using? If you click the Badge Data button at the top you can see the values that it is using.

Then on the Badge setting, you can choose the source here...

Can you post the review URL?
Try to create a new review template and take all the defaults. See if that one will work. Sometimes it will work on the front end but not when editing.
Just select both sources or unselect the one. It looks like the reviews were downloaded once, then later on a different download was done. If you go to the Review List page and use the All Source Pages filter you can see what that filter does.

"Select Reviews to Show" will overwrite all the other filter settings.
Make sure you have the correct Source selected or unselect to show all sources.

By default a review template will show all reviews in the Review List. First check the Display Order...

Then check the Filter Settings tab to make sure you are not Filtering out the reviews.

What method are you using to download the Google reviews? The Google Crawl should have owner response, the review funnel should also have them, but I have checked in a while. The Places API does not. Let me know the source of the Google reviews and I'll test on my site.
Customer support service by UserEcho
Which Google download method are you using and what are the search terms or place id?