Vijay Akula Thanks for posting this question in Microsoft Q&A. To start with, API Management is a fully managed service by Microsoft Azure and with platform as a service nature, we abstract many of the details and describe main components i.e., API gateway, a management plane, and a developer portal in detail. The creation process of the instance as well as APIs are internal and hence, they are not documented publicly.
Regarding compute question, APIM uses different compute platforms like stv1, stv2, mtv1 and those details are discussed in detail here in the tech community article as well as Compute platform for Azure API Management.
stv1 - Cloud Service (Classic)
stv2 - Virtual machine scale sets
mtv1 - App Service
Other than Compute, APIM also uses several other resources such as Azure SQL, Storage, Event Hub, Key Vault (for stv2) for the internal components and hence we would require outbound connectivity to these services listed here.
Does this help with your question? Feel free to add a comment for any other questions.