In Entity Framework Core, the Map method is used in advanced inheritance scenarios to configure specific mappings between an entity and a database table.

To implement a Table-Per-Concrete (TPC) inheritance strategy in Entity Framework, you need to override the OnModelCreating method in your DbContext class and configure the mappings for each concrete type separately.

In Table-per-Type (TPT) inheritance, each type in the hierarchy is mapped to a different database table. This means that each concrete type in the inheritance hierarchy gets its own table in the database, which can lead to a normalized database schema.

When choosing between TPH, TPT, and TPC inheritance strategies in Entity Framework, there are several performance considerations to keep in mind. TPH can result in wide tables with many nullable columns, which can impact storage and query performance, especially when dealing with large datasets. TPT requires additional joins for querying, potentially affecting performance, but it can provide better normalization and query performance compared to TPH in certain scenarios. TPC often leads to redundant data in multiple tables, increasing storage requirements and potentially affecting performance negatively. It's essential to analyze the specific requirements and trade-offs of each strategy to determine the most suitable one for a given scenario.

In advanced scenarios, you can customize the mapping of inheritance hierarchies beyond the default strategies provided by Entity Framework using the fluent API. This allows for fine-grained control over entity mappings, including specifying table names, column names, and relationships. Modifying the EDMX file directly is not recommended as it can be complex and error-prone. Customizing SQL queries or extending the base DbContext class may not provide the same level of flexibility as using the fluent API.

The primary use of stored procedures within Entity Framework is to enhance performance and security by reducing the amount of data sent between the database and the application, and by encapsulating business logic on the database server.

Functions can be executed directly in Entity Framework by using the DbContext's ExecuteFunction method, which allows invoking database functions mapped in the model.

In Entity Framework, stored procedures can be called by using the DbContext's Database property, which provides methods like ExecuteSqlCommand for executing SQL queries or stored procedures directly.

Using the Table per Hierarchy (TPH) strategy would be the most appropriate approach. TPH allows mapping all properties from all classes to a single database table, making it suitable for accommodating non-standard table structures in legacy databases. This simplifies the mapping process and aligns well with the existing database schema, reducing the need for extensive schema modifications. However, it's essential to consider potential performance implications, such as NULL values and table size, when implementing this strategy.

Table per Hierarchy (TPH) strategy would be chosen. TPH reduces the number of database tables required by mapping all properties from all classes to a single database table. This strategy simplifies the database schema, making it easier to manage and understand. However, it may result in NULL values for properties specific to certain derived types, impacting database performance and storage efficiency.

Indexing the Discriminator column in a Table-Per-Hierarchy (TPH) scenario can significantly improve query performance by quickly identifying the entity type.

Entity Framework has limitations when using stored procedures, such as limited support for advanced database features and restrictions on executing stored procedures with dynamic SQL statements.