The dimension table in a data warehouse provides context to the facts. It contains descriptive attributes and hierarchies that are used for filtering and grouping data in queries. This helps analysts and users understand the data in the fact table and answer various business questions.

In a Snowflake Schema, the design intentionally allows for some level of data redundancy to optimize query performance. This schema structure involves normalized dimension tables, which can lead to better storage efficiency and reduced data update anomalies, even though it may have some level of redundancy.

Data Integration Tools are essential for combining data from various sources, such as databases, flat files, and cloud services, and loading it into the data warehouse. These tools handle data extraction, transformation, and loading (ETL) processes, ensuring data consistency and quality.

To support in-depth sales data analysis with dimensions like region, product, and time, the best choice would be a Star Schema in the data warehousing architecture. OLAP Cubes are used to efficiently process complex queries and aggregations. Star Schema's simplicity and denormalized structure are well-suited for such analytical tasks.

Data Warehouse Appliances often ensure high data availability and fault tolerance by implementing a data replication strategy. This involves storing multiple copies of data or aggregations in different locations, which safeguards against data loss and system failure.

The phase of the evolution of data warehousing that involves gathering data from different sources and making it accessible in one place is known as "Data Integration." During this phase, data from diverse sources is collected, transformed, and loaded into the data warehouse to create a unified, accessible data repository for analytical purposes. Data integration is a crucial step in the data warehousing process.

Scaling out, also known as horizontal scaling, involves adding more machines or nodes to a system to handle increased load. It's a strategy used to improve a system's performance and capacity by distributing the workload across multiple resources.

In the ETL (Extract, Transform, Load) process, the first phase is "Extraction." This phase is responsible for gathering data from various sources, such as databases, flat files, and cloud sources, and extracting it for further processing and storage in a data warehouse.

For a startup concerned about upfront infrastructure costs and scalability, a cloud-based data warehouse is a suitable choice. Cloud solutions offer flexibility, scalability, and a pay-as-you-go model, reducing the initial investment. They can easily scale resources up or down as business needs evolve.

In OLAP (Online Analytical Processing) cubes, a dimension is defined by the combination of measures (such as sales, revenue), attributes (such as product names, customer names), and hierarchies (such as time periods). Dimensions are essential for structuring and analyzing data within an OLAP cube, providing a multi-dimensional view of the data.