To ensure that any objects uploaded to an S3 bucket are encrypted, you can implement Amazon S3 default encryption to make sure that any object being uploaded is encrypted before it is stored. Additionally, you can implement S3 bucket policies to deny unencrypted objects from being uploaded to the bucket. By setting the default encryption on the S3 bucket, you ensure that all new objects are encrypted automatically using server-side encryption. Using S3 bucket policies ensures that any upload requests that do not include encryption headers are denied, preventing unencrypted data from being stored.

To resolve the issue of random logouts in a stateful web application hosted on Amazon EC2 instances in an Auto Scaling group behind an Application Load Balancer (ALB) with a CloudFront distribution, two actions should be taken: configure cookie forwarding in the CloudFront distribution cache behavior and enable sticky sessions on the ALB target group. Cookie forwarding ensures that CloudFront passes user session information to the origin, while enabling sticky sessions on the ALB target group maintains user sessions by ensuring that subsequent requests from a user are directed to the same target.

To resolve the issue of 'too many connections' errors when a Lambda function attempts to connect to an Amazon RDS for MySQL DB instance, using Amazon RDS Proxy is the most appropriate solution. Amazon RDS Proxy acts as an intermediary between the application and the database, managing connection pools and reducing the number of direct connections to the database. This helps in handling a large number of simultaneous connections more efficiently by reusing existing connections, thus avoiding the maximum connections limit. Updating the connection string in the Lambda function to use the RDS Proxy will significantly improve connection management in this serverless architecture.

To ensure high availability and place the instances on distinct underlying hardware, the SysOps administrator should launch the instances into a spread placement group in a single AWS Region. Spread placement groups are designed to spread instances across distinct hardware to reduce the risk of simultaneous failures. Placement groups cannot span multiple AWS Regions, so the correct approach is to use a spread placement group within a single region.

The correct way to ensure the AWS CloudFormation template works in every region is to modify the template to use the 'Mappings' section. This section allows defining a map of region-specific values, which can include different AMI IDs for each region. By referring to the proper mapping within the template, the correct AMI for the respective region is used, thus resolving the issue of the template failing when the specified AMI does not exist in the target region.