Does Hubspot provides (out of the box) any monitoring view for incoming \outgoing integration messages like (RESTfull calls,SOAP..if exists...BulkAPI actions) etc.?
I'm not entirely sure I understand the question. Are you asking if HubSpot provides integration-consumable notifications of in-app changes? Or if HubSpot provides request monitoring?
If you're asking about the former, the Webhook API provides notifications for contact/company/deal creates/updates/deletes. If you're asking about the latter, Developer portals have a request monitoring page that allows you to view the requests being made by your integration. I've included the docs for both below: