The correct answers are B and D. Option B suggests updating the Lambda function in the API Gateway integration request to use the hotfix alias, and deploying the API Gateway to a new stage named 'hotfix' for testing, which ensures a separate testing environment without affecting the production setup. Option D involves modifying and testing the Lambda function, then publishing it as a new version, creating an alias 'hotfix' that points to this version, which ensures that the changes are not overwritten and provides a controlled environment for testing. Option C is incorrect because you can't use an unqualified ARN ($LATEST) to create an alias, emphasizing the necessity for a new version.