Hi there,
Thanks for reaching out with your questions about Google Listings & Ads!
>1. Does the plugin send the stock levels (quantity) to merchant center?
Google listings & ads does validate product availability when you configure your product feed in Merchant Center, but it does not maintain inventory levels.
More info about the specific sync data here: https://support.google.com/merchants/answer/7052112
>2. How often does the plugin sync with MC? or are there any triggers?
You can adjust your product “channel visibility” anytime, and the products will update automatically every 1-2 days.
More details here: https://docs.woocommerce.com/document/google-listings-and-ads/#channel-visibility
For triggers, they run automatically via ActionScheduler on your site. I supposed you can manually run the scheduled action to trigger a sync process.
More info here: https://docs.woocommerce.com/document/google-listings-and-ads/google-listings-and-ads-faqs/#section-8