Hi there,
I've worked on BigCommerce migrations as well as API integrations so I have experience in populating bigcommerce stores/dbs. I've read through the Meriin API doc that you have attached and it seems pretty straight forward in terms of pulling the product data that's required.
In terms of the real-time update, we can create an automated task on your host (requires us to create a cronjob task) to push changes/updates every minute or so.
If you have any questions prior to accepting my bid, please don't hesitate to message me here on freelancer.
Thanks for your consideration,
Shawn