It can, but I don't recommend it. The Review List, Templates, and Badges all have export CSV file buttons on them, then you can import the CSV file into the new site. The problem is that if you want to auto-update new reviews then you have to setup the download anyway so it's best to just re-download them to being with. That way they for sure have all the same page names. So, I would re-download the reviews and maybe move the templates if I spent a lot of time on them.

Another option would be to copy the data out of the MySql database and import it to the new database. You would need to be comfortable with modifying your WordPress database however. These are the tables you would look for...

wp_wpfb_badges
wp_wpfb_floats
wp_wpfb_forms
wp_wpfb_getapps_forms
wp_wpfb_gettwitter_forms
wp_wpfb_nofitifcation_forms
wp_wpfb_post_templates
wp_wpfb_reviewfunnel
wp_wpfb_reviews
wp_wpfb_total_averages

What's the Nextdoor URL you are using?

That would mean that your search terms or place id is incorrect. Try using this to find your Place ID...

https://wpreviewslider.com/two-methods-to-find-your-google-place-id/

Yeah, a review template by default will show all reviews on the review list that have text. Then you use the Filters to hide the ones you don't want to show. You can also use the "eye" icon on the Review List to hid a review from front side of the site.

I'm sorry that isn't possible with the plugin. 

If you added the fr language code then it should be okay.

Okay, so are you good to go now or do you still need help?

Which Google download method are you using? Get Reviews > Google Crawl, Get Reviews > Google Places API, or the review funnel? What are the search terms or place id you are using?

That is only used for Submitted reviews, not downloaded reviews since you can't give consent to someone.

It looks like you are using a bunch of custom CSS on this review template. What exactly are you trying to make it look like? There isn't going to be an easy way to move the name below the review text just using CSS.