Answer: A, B, D
Option A is correct. AWS API Gateway can integrate with any HTTP-based endpoints available over the internet.
Q: With what backends can Amazon API Gateway communicate?
Amazon API Gateway can execute AWS Lambda functions in your account, start AWS Step Functions state machines, or call HTTP endpoints hosted on AWS Elastic Beanstalk, Amazon EC2, and also non-AWS hosted HTTP based operations that are accessible via the public Internet. API Gateway also allows you to specify a mapping template to generate static content to be returned, helping you mock your APIs before the backend is ready. You can also integrate API Gateway with other AWS services directly. For example, you could expose an API method in API Gateway that sends data directly to Amazon Kinesis.
Option B is correct. AWS can use Lambda function from another account as an integration type.
Option C is incorrect. AWS API gateway can connect to AWS services, making proxy calls only to their respective AWS APIs. There is no integration type for database connections directly from API Gateway. You can use the Lambda function to connect with the database and make Lambda as an integration type for API Gateway.
Option D is correct. AWS has introduced VPC Link, a way to connect to the resources within a private VPC.Refer to the documentation here for more information on VPC Links. https://aws.amazon.com/blogs/compute/introducing-amazon-api-gateway-private-endpoints/