Explanation
The system requirement is to expose data from the on-premise applications to Salesforce for a more unified user experience in real-time. The possible actions that can fulfill this requirement are:
Answer B is valid because developing custom APIs on the company's network that are invokable by Salesforce can allow Salesforce to access the data from the on-premise applications in real-time. However, this action requires opening a firewall port or using a reverse proxy to allow Salesforce to communicate with the on-premise APIs securely3 Answer C is valid because deploying MuleSoft to the on-premise network and designing externally facing APIs to expose the data can also enable Salesforce to access the data from the on-premise applications in real-time. MuleSoft is an integration platform that can connect various systems and applications using APIs and standard protocols. MuleSoft can also handle security, orchestration, transformation, and other integration aspects.
Answer A is not valid because developing an application in Heroku that connects to the on-premise database via an ODBC string and VPC connection is not a real-time solution. Heroku is a cloud platform that can host web applications and services, but it cannot expose data from an on-premise database directly to Salesforce. To use Heroku for this purpose, an ETL tool or a middleware solution would be needed to synchronize the data between the on-premise database and Heroku, which would introduce latency and complexity to the integration.
Answer D is not valid because running a batch job with an ETL tool from an on-premise server to move data to Salesforce is also not a real-time solution. ETL stands for extract, transform, and load, which is a process of moving data from one system to another in batches. ETL tools can be used for data migration or integration, but they cannot provide real-time access to data from on-premise applications to Salesforce. ETL tools also have limitations on data volume, frequency, and reliability.
1: Bulk API Limits 2: Bulk API Features 3: Integrating with Salesforce using Custom Web Services :
MuleSoft Overview : Heroku Overview : ETL Overview

Explanation
The continuation class in Apex allows you to make long-running requests to external web services and process their responses in a callback method. This is useful for scenarios where the response time exceeds the normal Apex limits, such as 10 seconds for synchronous transactions or 120 seconds for asynchronous transactions. By using continuation, you can avoid hitting these limits and provide a better user experience1 References: Callout Limits and Limitations

Explanation
The HttpCalloutMock interface allows testing HTTP callouts by returning a predefined response in a test context.
By implementing HttpCalloutMock to return responses per RAML specification, the Apex REST API Clients unit tests can confirm that the API requests and responses match the expected format and values.
Calling the Apex REST API Clients in a test context to get the mock response is also necessary to verify the adherence to the RAML specs. Calling the HttpCalloutMock implementation from the Apex REST API Clients or requiring the Apex REST API Clients to implement the HttpCalloutMock are not valid options because the HttpCalloutMock interface is implemented by a separate class that is passed as a parameter to the Test.setMock method2 References: 1: Idempotent REST APIs 2: Testing HTTP Callouts by Implementing the HttpCalloutMock Interface