Flutter supports cross-platform functionality for IoT systems by employing a shared codebase using the Dart programming language. Dart allows developers to write code once and run it on multiple platforms, including iOS and Android. This approach streamlines development, reduces code duplication, and ensures consistent behavior across different devices, making it an effective strategy for building IoT applications with Flutter.

A common issue faced when dealing with different device screen sizes and resolutions in cross-platform development is layout and responsiveness challenges. Ensuring that the user interface adapts appropriately to various screen sizes is crucial for a consistent user experience. Developers need to implement responsive design practices, utilize flexible layouts, and leverage platform-specific tools to address these challenges and create applications that look and feel native on diverse devices.

Using platform channels in Flutter is crucial for integrating with device features by facilitating communication between Dart code and native code. Platform channels provide a structured interface for data exchange, allowing Flutter apps to leverage native functionality seamlessly. This is essential when interacting with platform-specific APIs, accessing device sensors, or integrating features that require native code execution. Understanding the significance of platform channels is key to building robust and feature-rich Flutter applications.

In advanced state management, 'immutable state' refers to state objects that cannot be modified after creation. Once an immutable state object is created, its values cannot be changed. This characteristic ensures predictability and helps prevent unexpected side effects. Immutable state is often used in state management architectures like Redux to enhance application stability and facilitate efficient state handling in complex applications.

In the BLoC architecture, StreamControllers are used to send events from the UI to the business logic component. A StreamController allows the UI to dispatch events to the BLoC, triggering the corresponding business logic. It serves as a communication channel between the UI layer and the BLoC, facilitating the flow of data and events in a reactive and asynchronous manner. Understanding the role of StreamControllers is key to implementing effective BLoC patterns.

The primary class used for theming a Flutter application is ThemeData. It is a class in Flutter that represents the overall theme of the application, including colors, fonts, and other visual elements. By defining a ThemeData object, developers can maintain a consistent and aesthetically pleasing design throughout their app. Understanding how to use and customize ThemeData is essential for creating visually cohesive Flutter applications.

To mock network requests in Flutter unit tests, a custom mock server can be created. This involves creating a mock implementation of the server that responds to requests with predefined responses. Alternatively, developers can use libraries like http package's mock library to simulate network behavior. Mocking network requests is essential for testing app behavior under various network conditions and ensuring the reliability of Flutter applications.

To run a Flutter app on an iOS simulator or Android emulator, you use the command 'flutter run'. This command compiles the Flutter app and launches it on the specified emulator or connected device. Understanding how to use 'flutter run' is essential for testing and debugging Flutter applications during development, allowing developers to see their app in action on different platforms.

In Flutter, the 'TextField' widget is used to capture text input from users. It provides a space for users to enter and edit text. Developers can customize the appearance and behavior of the 'TextField' to suit their application's requirements. Understanding how to use 'TextField' is essential for building forms, search bars, and various input scenarios in Flutter applications.

Advanced data visualization in Flutter for representing IoT data involves leveraging Flutter's canvas and custom painting capabilities. Developers can create highly customized visualizations by drawing directly on the screen. This technique allows for intricate and tailored representations of IoT data. While third-party charting libraries are available, using Flutter's native features provides a high level of flexibility and control over the visual presentation of complex IoT data.