Correct Answers: C and D
Option A is incorrect. Controlling access to your back-end database running on Aurora will not restrict access to your API Gateway REST endpoint. Access to your API Gateway REST endpoint must be controlled at the API Gateway and VPC level.
Option B is incorrect. The Gateway VPC Endpoint is only used for the S3 and DynamoDB services.
Option C is correct. You can make your REST APIs private by using the aws:SourceVpce condition in your API Gateway resource policy to restrict access to only your VPC Endpoint.
Option D is correct. Use a VPC Interface Endpoint to restrict access to your REST APIs to traffic that arrives via the VPC Endpoint.
Option E is incorrect. The aws:SourceArn condition key is not used to restrict access to traffic that arrives via the VPC Endpoint.
References:
Please see the Amazon API Gateway developer guide titled Creating a private API in Amazon API Gateway (https://docs.aws.amazon.com/apigateway/latest/developerguide/apigateway-private-apis.html), the Amazon API Gateway developer guide titled Example: Allow private API traffic based on source VPC or VPC endpoint (https://docs.aws.amazon.com/apigateway/latest/developerguide/apigateway-resource-policies-examples.html#apigateway-resource-policies-source-vpc-example), the Amazon Aurora user guide titled Amazon Aurora security (https://docs.aws.amazon.com/AmazonRDS/latest/AuroraUserGuide/Aurora.Overview.Security.html), the Amazon Aurora user guide titled Amazon Aurora DB clusters (https://docs.aws.amazon.com/AmazonRDS/latest/AuroraUserGuide/Aurora.Overview.html), the Amazon Aurora user guide titled Aurora DB instance classes (https://docs.aws.amazon.com/AmazonRDS/latest/AuroraUserGuide/Concepts.DBInstanceClass.html), the Amazon API Gateway developer guide titled AWS condition keys that can be used in API Gateway resource policies (https://docs.aws.amazon.com/apigateway/latest/developerguide/apigateway-resource-policies-aws-condition-keys.html), and the Amazon Virtual Private Cloud AWS PrivateLink page titled VPC endpoints (https://docs.aws.amazon.com/vpc/latest/privatelink/vpc-endpoints.html)