For User_DataProcessor in Account B to access the S3 bucket in Account A, two key steps are needed. Firstly, Account A needs to add a policy to the S3 bucket that explicitly allows the IAM user from Account B the necessary permissions to access the bucket. This is achieved by specifying the principal as the IAM user and granting the required actions, as shown in option C. Secondly, Account B must assign an IAM policy to User_DataProcessor that grants permission to perform the required actions (GetObject and ListBucket) on the S3 bucket in Account A, which is specified in option D. Together, these steps ensure that cross-account access is correctly configured.

To design a cost-effective serverless architecture that minimizes operational complexity while refactoring a traditional web application as microservices, using Amazon Elastic Container Service (ECS) with the Fargate launch type is a suitable solution. ECS with Fargate allows automatic scaling of containers based on the load, which handles the variable workload effectively. By uploading the container images to Amazon Elastic Container Registry (ECR) and deploying tasks from these images, the operational management is streamlined. Configuring two auto-scaled ECS clusters ensures separate environments for production and testing. Additionally, using Application Load Balancers to direct traffic to the ECS clusters aids in efficiently distributing the load. This solution fully leverages AWS managed services, reducing the overall operational burden and cost.

To achieve an automatic failover to the backup region and maintain an RTO of less than 15 minutes within a limited budget, the solution should include mechanisms for monitoring the primary region and taking swift action if it becomes unhealthy. Configuring an AWS Lambda function in the backup region to promote the read replica and modify the Auto Scaling group values of instances ensures that resources can quickly be provisioned in the backup region when needed. Using Route 53 with a health check to monitor the web application and sending an SNS notification to trigger the Lambda function when the primary region is unhealthy allows traffic to be rerouted to the backup region promptly. This setup avoids the need for an expensive active-active strategy while providing the necessary failover capability.

To ensure automatic recovery from failure with minimal downtime, several steps can be taken. First, using an Elastic Load Balancer to distribute traffic across multiple EC2 instances and ensuring these instances are part of an Auto Scaling group with a minimum capacity of two instances can help maintain application availability if one instance fails. Then, modifying the DB instance to create a Multi-AZ deployment ensures that the database remains available by automatically failing over to a secondary availability zone in the event of an issue. Finally, creating a replication group for the ElastiCache for Redis cluster and enabling Multi-AZ on the cluster ensures that the in-memory data store is resilient and can fail over to another availability zone if necessary. This combination achieves a robust, highly available architecture capable of automatically recovering from failures with minimal downtime.

To provide a custom error page instead of the standard ALB error page with the least operational overhead, two steps are necessary. First, create an Amazon S3 bucket to host a static webpage and upload the custom error pages to that S3 bucket. This allows for a highly-available location to store the error pages. Second, configure a CloudFront custom error page to handle the custom error responses effectively. This setup leverages existing services with minimal additional configuration, offering an efficient and scalable solution without the need for complex DNS changes or handling custom code for each error.