Currently running eCommerce platform with Magento. Want to see if it is possible to manage inventory via third party API. Want the system to automatically send order API to third party program, and also receive and update new data from third party.
The short answer is Yes, it is possible. You can treat an external platform, like an ERP, OMS, WMS, POS, or Inventory Management software as your data master for product and inventory data. Similarly, orders can flow between your two systems via Magento's API. This is all pretty common.
Depending on what system you're trying to connect via API, there may already be existing connectors available in the Magento Marketplace, or through other sources, such as integration Platform as a Service (iPaaS) providers.