Explanation:

Why B is correct
The Partner WSDL is loosely typed and org-agnostic. It works with generic sObject types and name-value pairs, so it does not embed any org-specific objects or fields. That makes it the right choice when one integration must serve multiple Salesforce orgs whose metadata differs (different custom objects and fields), such as an ISV or a central system connecting to many customer orgs.

The client discovers the org's schema at runtime with describeSObjects and describeGlobal, so custom fields added or removed in an org do not break the integration and do not require regenerating the WSDL.

Why A is wrong
The Enterprise WSDL is strongly typed and generated for one specific org. It includes that org's custom objects and fields as typed classes, which makes coding easier and safer at compile time. The tradeoff is that it is tied to that org's metadata, so the client must be regenerated when the schema changes, and it will not work cleanly across orgs with different metadata.

Why C is wrong
"SOAP API WSDL" is not a distinct WSDL choice. The Enterprise and Partner WSDLs are both WSDLs for the SOAP API, so this option doesn't identify which one to use. (The Metadata WSDL and others exist for different purposes.)

Reference
SOAP API Developer Guide: Enterprise and Partner WSDL, Choosing a WSDL
Trailhead: Salesforce APIs concepts in the integration learning modules

Explanation:

The key distinction is record-sharing/record-access behavior among the different Streaming API event types.

Change Data Capture (CDC) does not support record-sharing access checks. Salesforce's event comparison specifically lists:

CDC: Record-sharing support = No
PushTopic: Record-sharing support = Yes
Platform Events: Not applicable in the same record-change sense
Generic Events: Not applicable

Therefore, B is correct.

Why A is incorrect

A. PushTopic Events can define a custom payload. ❌
PushTopic notifications are based on a SOQL query. The fields selected in the query determine the fields included in the notification. They don't provide the same user-defined custom payload capability as Platform Events.

For example:

SELECT Id, Name, Status__c FROM Account

The selected fields form the notification payload.

Platform Events, rather than PushTopics, are designed for custom event schemas and user-defined payloads.

Why C is incorrect

C. Change Data Capture can be published from Apex. ❌
CDC is automatically generated when changes occur to objects that are enabled for CDC. It isn't a custom event that you publish manually from Apex.

By contrast, Platform Events can be published through Apex. Salesforce explicitly lists Apex publishing as supported for Platform Events but not CDC.

Explanation:

Why A is correct
The trigger has failed since the day it went to production. The symptom is a failing subscriber, and the way to see why is to monitor the trigger's execution. Platform event triggers run asynchronously as a special Automated Process user, not as the user who published the event. To capture their logs, you add a trace flag for the Automated Process entity in Setup > Debug Logs. The logs show governor limit usage, exceptions, and where the trigger fails, which tells you whether the cause is bad data, a null field, a limit breach, or something else. Without that monitoring in place, failures in this decoupled, asynchronous flow are largely invisible.

You can complement this with:

Event Monitoring or the EventBusSubscriber object, to check subscriber state, position, and retry status.
Trigger design for failures: platform event triggers can be retried with EventBus.RetryableException, up to 9 times, and checkpointing with EventBus.TriggerContext.setResumeCheckpoint() keeps the trigger from reprocessing already-handled events.

Why B is wrong
The platform event is its own object with its own fields. It is not meant to mirror the Lead definition, and no requirement says the two must match. A field mismatch could be a cause of failure, but that is a design check, not a type of monitoring.

Why C is wrong
Publishing and delivery allocations are worth watching, and exceeding them causes publish errors. But that would affect publishing, whereas here the events are being published and it is the trigger that fails. The limit monitoring wouldn't reveal the trigger's exception.

Reference
Platform Events Developer Guide: Debug Platform Event Triggers, Platform Event Triggers (retry and checkpoint)
Salesforce Help: Set Up Debug Logging

Explanation:

1. Why B is Correct (Handling Long-Running Asynchronous Processes & Gateway Constraints)

API Gateway and Platform Timeouts:
The external eligibility systems take up to 90 seconds to return a response, but the customer's API Gateway enforces a strict 9-second timeout constraint. Additionally, standard synchronous Apex callouts have a maximum 10-second timeout limit, and even Continuations cap out well below 90 seconds. Any synchronous or blocking request-reply mechanism will inevitably fail.

Asynchronous Decoupling via Platform Events:

Salesforce initiates the request asynchronously.

MuleSoft processes the request against the external eligibility systems over the 90-second window without blocking a user thread or hitting gateway timeouts.

Once the response is ready, MuleSoft publishes the result back into Salesforce via a Remote Call-In using Platform Events.

The Salesforce Lightning UI listens for these events in real-time using the empAPI (CometD streaming), cleanly notifying the agent when processing completes.

2. Why the Other Options are Incorrect

A. Recommend synchronous Apex callouts from Lightning UI to External Systems via Mule and implement polling on an API Gateway timeout:
Synchronous callouts and polling are entirely unsuited for a 90-second process governed by a hard 9-second API Gateway timeout. Polling over synchronous REST endpoints would exhaust platform CPU time, hit governor limits, and cause frequent gateway timeouts.

C. Use Continuation callouts to make the eligibility check request from Salesforce Lightning UI at page load:
While Continuations handle long-running callouts by suspending threads, they still rely on an open underlying HTTP request channel that must respect the API Gateway's strict 9-second timeout limit—meaning the gateway would drop the connection long before the 90-second backend process finishes.

Explanation:

The requirement is a temporary, short-term solution during an org merger: new leads created in the retiring org (via website forms) must appear in the new Salesforce org within 30 minutes, with the least amount of development effort.

Calling the standard Salesforce REST API from the retiring org (for example, via a simple Flow, Process Builder, or lightweight Apex trigger that performs an HTTP callout) is the simplest approach:

Uses the native Lead resource (/services/data/vXX.0/sobjects/Lead).
Requires minimal (or zero) custom code.
Easily meets the 30-minute latency requirement (near real-time is possible, but 30 minutes allows for simple scheduling or asynchronous processing if needed).
Leverages existing OAuth/Named Credential authentication between the two orgs.

Why the other options require more effort

B. Use the Tooling API with Process Builder to insert leads in real time.
The Tooling API is designed for metadata and development tooling, not for inserting business records such as Leads. This is not a valid or practical pattern and would require unnecessary custom work.

C. Use the Composite REST API to aggregate multiple leads in a single call.
The Composite API is useful for reducing round-trips when creating related records or performing multiple operations in one request. For a simple “create Lead in another org” requirement, it adds complexity without providing meaningful benefit and requires more development effort than a straightforward single-record REST call.

Key takeaway
For a temporary cross-org Lead sync with a 30-minute SLA, the lowest-effort solution is a direct call to the standard Salesforce REST API to insert the Lead into the target org.