Sonia,
Does APIM developer portal allow users to subscribe/unsubscribe to API/plans/products/packages without developer registration?
It's required to have a registered user and an organization that they are a member of in order for the user to be able to register their application with APIs, Account Plans, and API Plans.
Does APIM developer portal allow registered App developers to subscribe/unsubscribe to APIs visible to them with or without approval mechanism?
A developer would first need to register an application. Application approval is enabled by default, but you can turn off the application approval process. Once a developer has a registered and approved application, they can subscribe to any public API that is available. You can also have private APIs, but they would need to be associated with the developer's organization before the developer can associate the private API with their application.
How to configure the approval process
Does APIM developer portal provide App developers (consumers) functionality to test APIs before subscribing them?
The API Developer Portal has a built in test client called "API Explorer" which allows consumers to test APIs. If the APIs being tested don't require an API Key or other possible authentication methods, then you don't need to have an application associated with them in order to test them. If the APIs do require an API Key or other authentication methods, then you can still test the API, but you will likely get authentication failures as a response from the API.
Can App developers customize their dashboards based on their preferences?
The only dashboard customization that is available is to enable or disable widgets that display on the dashboard main page.
Let me know if you'd like me to elaborate on any of the points above.
--Azad