There are no hooks or filters built into the plugin for that. All the reviews are stored in a custom table in your wp database, so you could just code something that looks at that table on a cron job and send any updates along.

Sorry, that currently isn't built in to the plugin. I can add it to my list of feature requests. In the meantime, you can get it to send an email when you get a review, then you could use some sort of automation tied to your email account.

What is the Place id? Also, send me a link to the reviews on Google.

Can you tell me the settings you are using so I can download and test on my server?

If you have version  12.6.8 then there should be a location field you can turn on. 

Then you can turn it on the Review Template with this setting...

You can check it on the Review List here...

Double-check the Filter settings, especially the source page, and make sure they are not being filtered out. You can turn off all filters to check. By default, a review template will show all reviews in the review list. Then you set the Filters to start hiding the ones you don't want to show.

Not sure I understand. Please explain what you are trying to accomplish and for what purpose. There may be a better way to do it.