When server-side load-balanced TLS mutual authentication is required between API implementations and API clients
*****************************************
Fact/ Memory Tip: Although there are many benefits of CloudHub Dedicated Load balancer, TWO important things that should come to ones mind for considering it are:
>> Having URL endpoints with Custom DNS names on CloudHub deployed apps
>> Configuring custom certificates for both HTTPS and Two-way (Mutual) authentication.
Coming to the options provided for this question:
>> We CANNOT use DLB to perform cross-region load balancing between separate deployments of the same Mule application.
>> We can have mapping rules to have more than one DLB URL pointing to same Mule app. But vicevera (More than one Mule app having same DLB URL) is NOT POSSIBLE
>> It is true that DLB helps to setup custom DNS names for Cloudhub deployed Mule apps but NOT true for apps deployed to Customer-hosted Mule Runtimes.
>> It is true to that we can load balance API invocations across multiple CloudHub workers using DLB but it is NOT A MUST. We can achieve the same (load balancing) using SLB (Shared Load Balancer) too. We DO NOT necessarily require DLB for achieve it.
So the only right option that fits the scenario and requires us to use DLB is when TLS mutual authentication is required between API implementations and API clients.

Correct answer: Unit tests (Whitebox)
*****************************************
Reference:
As per general IT testing practice and MuleSoft recommended practice, Integration and Performance tests should be done on full end to end setup for right evaluation. Which means all end systems should be connected while doing the tests. So, these options are OUT and we are left with Unit Tests and Functional Tests.
As per attached reference documentation from MuleSoft:
Unit Tests - are limited to the code that can be realistically exercised without the need to run it inside Mule itself. So good candidates are Small pieces of modular code, Sub Flows, Custom transformers, Custom components, Custom expression evaluators etc.
Functional Tests - are those that most extensively exercise your application configuration. In these tests, you have the freedom and tools for simulating happy and unhappy paths. You also have the possibility to create stubs for target services and make them success or fail to easily simulate happy and unhappy paths respectively.
As the scenario in the question demands for API implementation to be tested before deployment to Staging and also clearly indicates that there is enough/ sufficient amount of mock data to test the various components of API implementations with no active connections to the backend systems, Unit Tests are the one to be used to incorporate this mocked data.

Implement different system APIs named createCustomer, amendCustomer, retrieveCustomer
and suspendCustomer as they are modular and has seperation of concerns
*****************************************
>> It is quite normal to have a single API and different Verb + Resource combinations. However, this fits well for an Experience API or a Process API but not a best architecture style for System APIs. So, option with just one customerManagement API is not the best choice here.
>> The option with APIs in createCustomerInCRMZ format is next close choice w.r.t modularization and less maintenance but the naming of APIs is directly coupled with the legacy system. A better foreseen approach would be to name your APIs by abstracting the backend system names as it allows seamless replacement/migration of any backend system anytime. So, this is not the correct choice too.
>> createCustomer, amendCustomer, retrieveCustomer and suspendCustomer is the right approach and is the best fit compared to other options as they are both modular and same time got the names decoupled from backend system and it has covered all requirements a System API needs.