A NoSQL Database would be the best fit for this scenario. NoSQL databases, especially those designed for document storage, provide scalability and flexibility for handling diverse product information. The ability to store and retrieve complex data, including images and descriptions, aligns well with the requirements of an e-commerce platform.

In Dimensional Modeling, a Dimension table contains descriptive attributes used for analysis. These attributes provide context and additional information about the measures in the Fact table. For example, in a sales data warehouse, a Date Dimension table might contain attributes like year, quarter, and month.

In a Key-Value Store, the Key is used to uniquely identify each value. The key serves as a unique identifier that allows efficient retrieval of the associated value. This simplicity is one of the key advantages of Key-Value Stores.

Snowflake Schema typically has higher data redundancy compared to a Star Schema. In a Snowflake Schema, data is normalized into multiple tables, resulting in more duplicate data across different tables. In contrast, a Star Schema denormalizes data into a single table for each dimension, reducing redundancy.

In a distributed Key-Value Store, replication is crucial for ensuring data availability and fault tolerance. By storing multiple copies of data across different nodes, the system can continue to function even if some nodes fail, ensuring high availability and resilience against faults.

Performance profiling is a technique used in database performance tuning to analyze and identify bottlenecks in the system. It involves monitoring and measuring various aspects of the database, such as query execution times, resource usage, and query plans. Profiling helps in understanding where the performance issues lie and allows for targeted optimizations to improve overall system performance.

Lossless compression reduces the storage size of data without losing any information. It is commonly used when it's important to preserve all the original data, such as in databases or text files. Unlike lossy compression, there is no loss of quality in the compressed data.

In a fact table, each record represents a transaction at a specific level of detail. A fact table contains quantitative data, such as measurements or metrics, and is typically associated with a timestamp to capture when the transaction occurred. This helps in analyzing and understanding the details of specific events or transactions in the dataset.

In this scenario, the best approach is to use a superclass-subclass relationship. By having a staff superclass and professor/administrative staff subclasses, you can inherit common attributes from the superclass while allowing specific attributes for each subclass. This promotes data integrity and reduces redundancy.

For a financial institution analyzing complex customer data, Snowflake Schema may be more appropriate. Snowflake Schema's normalization reduces redundancy and ensures data integrity, crucial in financial operations where accuracy is vital. It accommodates intricate relationships among entities like customers, transactions, and demographics, facilitating comprehensive analysis and reporting.