The Separation of Concerns (SoC) is a fundamental design principle in ASP.NET Core MVC. It advocates for dividing the application into distinct and separate components, where the Model handles data, the View manages the presentation, and the Controller orchestrates the flow of data between them. This separation enhances maintainability, testability, and scalability.

Razor Layout Views in ASP.NET Core are primarily used to define the common structure or layout that multiple Razor views within your application will share. This allows you to maintain a consistent look and feel across various parts of your web application. They help separate the presentation logic from the content-specific views.

In the MVC (Model-View-Controller) design pattern, the Controller is primarily responsible for handling user input and interactions. It receives user requests, processes them, interacts with the Model to retrieve or manipulate data, and determines the appropriate View to render as a response.

The Identity middleware in ASP.NET Core primarily handles authentication. It intercepts requests to determine if a user is authenticated and provides features like cookie-based authentication, token-based authentication, and integration with external identity providers (e.g., Google, Facebook) for user login.

The primary language used for coding in ASP.NET Core is C#. While ASP.NET Core supports multiple languages, C# is the most commonly used language for building ASP.NET Core applications due to its strong integration with the framework and extensive tooling support.

To restrict access to registered users only, you would use the [Authorize] attribute. This attribute can be applied at the controller or action level and ensures that only authenticated users can access the specified resources. It doesn't require specifying roles, as it already implies authenticated users. [AllowAnonymous] would allow both anonymous and registered users, while [Authorize(Roles = "Admin")] and [Authorize(Roles = "User")] are role-based authorizations and are not suitable for this scenario.

In the MVC (Model-View-Controller) architecture, the 'Model' component handles data-related logic, such as fetching data from a database. It represents the application's data and business logic. The 'Controller' handles user input and coordinates the flow of data between the 'Model' and 'View' components.

To preserve the user's cart information across sessions, even after they log out, you should utilize Session state with server-side storage. This allows the cart data to be stored on the server, making it persistent across user sessions.

Project.json handled transitive dependencies explicitly, meaning it included both direct and transitive dependencies in the project file. In contrast, the NuGet approach in previous ASP.NET versions handled transitive dependencies implicitly, which required developers to manage them manually. Project.json's explicit handling improved transparency and control over dependencies.

The "Build Scripts" would NOT typically be found in the project.json file. Project.json primarily focused on project structure, dependencies, and target frameworks, whereas build scripts were typically defined in other build-related files or tools specific to the build system.