Explanation
Streaming API is the best option for sending real-time notifications of changes to Salesforce data. Streaming API uses a publish-subscribe model to push relevant data to subscribers without polling. Streaming API supports PushTopic events, which are based on SOQL queries that define the data changes to listen for. The affiliate company can subscribe to a PushTopic event on the NTO Salesforce org and receive notifications whenever the data that matches the query changes. This way, the affiliate company can be informed of any updates to the opportunities in the NTO Salesforce instance.

Explanation
Integrating Salesforce with Data Warehouse, Order Management and Email Management System is the best option considering Salesforce capabilities. Salesforce can be used as the primary case management system, replacing the existing one. Salesforce can also integrate with the Data Warehouse to provide analytics and reporting on case data. Salesforce can integrate with the Order Management System to access order information related to cases. Salesforce can integrate with the Email Management System to send and receive emails from customers and agents. Reference: Salesforce Integration Architecture Designer Resource Guide, page 16

Explanation
The authentication is achieved by handling it in the code. A Named Credential is a type of metadata that specifies the URL of a callout endpoint and its required authentication parameters. An Apex callout is a way to invoke an external web service or API from Apex code. When using a Named Credential with an Apex callout, the authentication is handled by the Apex code that invokes the callout. The Apex code can use the HttpRequest class to set the endpoint, method, headers, and body of the callout request, and use the Http class to send the request and receive the response. The Apex code can also use the NamedCredential class to access the properties of the Named Credential, such as the principal type, protocol, and credential type. Handling authentication with login flows is not a valid option because login flows are a way to customize the user login process in Salesforce, not for external web services or APIs. Connecting via Salesforce Connect or Communities is not a valid option because they are not related to Apex callouts or Named Credentials.

https://developer.salesforce.com/docs/atlas.en-us.api_streaming.meta/api_streaming/using_streaming_api_durability.htm