Challenges in storage optimization for cloud-based databases include limited control over the underlying infrastructure. Cloud providers manage the hardware, making it essential for organizations to adapt to the cloud environment and optimize storage within the constraints of the chosen cloud platform.

In data warehousing, a degenerate dimension is a dimension key that does not have its own dimension table but is instead stored in the fact table. It's essentially a dimension attribute that is treated as a measure due to its significance in analysis. Understanding this is crucial for designing efficient data warehouses.

The process of loading data into a Data Warehouse or Data Mart is known as ETL (Extract, Transform, Load). This involves extracting data from source systems, transforming it into a suitable format, and loading it into the target data repository for analysis and reporting.

In a fact table, surrogate keys are used instead of natural keys to uniquely identify each record. Surrogate keys are system-generated and provide a stable identifier, avoiding the complexities that can arise with changes in natural keys. This enhances the stability and efficiency of the data warehouse.

Dimensional Modeling contributes to data warehouse performance by reducing data redundancy, simplifying complex queries, and providing efficient aggregations. This design approach optimizes query performance and facilitates faster data retrieval, which is crucial for data warehouse efficiency.

The NOT NULL constraint ensures that a column does not contain NULL values. It is used to enforce data integrity by requiring each value in the specified column to be filled with valid data.

For storing user profiles with varying attributes, a Document Store is recommended. Document stores, like MongoDB, allow flexible schema design, making it suitable for dynamic data structures like user profiles with different attributes. It provides efficient retrieval and storage of unstructured data.

Factors like query performance requirements are crucial when deciding to denormalize a database schema. Understanding the specific needs of the application, including read and write patterns, helps in making informed decisions about when and how to denormalize.

Advantages of using inheritance in database modeling include improved data consistency and reduced redundancy. However, disadvantages may arise from increased complexity and potential performance issues, making it crucial to carefully consider when to use inheritance.

Denormalization can lead to improved retrieval performance for certain types of queries. By minimizing the need for joins and simplifying data structures, queries that involve reading data become more efficient in a denormalized schema.