The solution that meets the requirements with minimal effort involves creating RDS event subscriptions. The tracking systems can then subscribe to specific RDS event system notifications. This approach is straightforward and directly aligns with the need to track various database operations such as shutdown, deletion, creation, and backup. It utilizes built-in features of RDS, ensuring minimal configuration and maintenance overhead.

The best approach for securely managing database credentials in this context is to use AWS Secrets Manager. Secrets Manager allows for centralized credentials management with automatic rotation, ensuring the credentials are updated every 60 days as required. By restricting permissions on the secrets to only the IAM role associated with the instance profile, the credentials are kept secure. The application can retrieve these credentials from Secrets Manager at start-up, ensuring that it always uses the latest credentials without manual intervention, mitigating security risks associated with storing credentials in text files or AMIs.

To secure the cache data and protect it from unauthorized access in Amazon ElastiCache for Redis, it is essential to implement several security measures. Enabling in-transit and at-rest encryption ensures that data is encrypted both when it is being transmitted and when it is stored, protecting it from eavesdropping and unauthorized access (A). Configuring the security group to allow inbound traffic only from trusted clients on the specific port (6379) helps restrict access to trusted sources and adds an extra layer of security (C). Additionally, creating the cluster with the auth-token parameter ensures that only users or applications with the correct token can access the Redis commands, providing further security against unauthorized access (F).

To migrate a 1 TB RDS for PostgreSQL DB instance to an Amazon Aurora PostgreSQL DB cluster with minimal downtime, the fastest way is to use an Aurora Replica. By creating an Aurora Replica of the RDS instance, you can keep the replica synchronized with the source database. During the cutover, you promote the Aurora Replica to master, minimizing downtime since there's no need to wait for a full backup and restore process. This approach provides a seamless and speedy migration path.

For optimal performance when migrating databases, the AWS DMS replication instance should be placed in the same VPC and Availability Zone as the target database instance. This minimizes data transfer times and potential latency issues, especially given that the replication instance will need to load large amounts of data into the target. Additionally, placing the replication instance near the target database can simplify network configurations and ensure a more efficient migration process.