The lifecycle method that runs immediately after a component's output is rendered to the DOM in React is componentDidMount. This is where you can perform actions that require interaction with the DOM, like setting up timers or fetching data from an API.

The primary purpose of the Render Props pattern is to allow for communication between components. It enables components to share data or logic in a flexible way, making it a powerful technique for building reusable and composable components. With Render Props, components can communicate and pass information, enhancing the flexibility and reusability of the code.

To improve performance when dealing with a large list of items, each with its own click handler, you should implement event delegation. This involves attaching a single event handler to a common ancestor of the list items. This way, you can handle all click events efficiently without the overhead of attaching individual handlers to each item. The other options are not effective performance optimization strategies in this context.

In React Transition Group, the prop used to define the duration of an exit animation is exitDuration. This prop allows you to control how long it takes for a component to animate out of the view when it's being removed. The other options (transitionDuration, animationDuration, and duration) are not specific to exit animations in React Transition Group.

To prevent unnecessary re-renders when consuming context, you can use memoization techniques like React.memo(). This higher-order component wraps the component and only re-renders it when its props or context values change. It's a performance optimization technique to avoid unnecessary re-renders, especially when the component depends on context values. The other options are not related to preventing re-renders due to context consumption.

To achieve an efficient update of the cart total in response to changes in items or their quantities, you would use Reactions in MobX. Reactions are triggered automatically when observable data they depend on changes. In this case, a reaction can recalculate the cart total whenever the cart items or their quantities change, ensuring an automatic and efficient update.

In the context of React and Redux, 'immutable state' refers to state that cannot be changed after it's created. In Redux, state immutability is a core principle. Instead of modifying the existing state, a new state object is created with the desired changes. This immutability ensures predictability and helps in tracking state changes, making debugging and testing easier.

React Portals, despite their ability to exist anywhere in the DOM tree, behave like normal React children when it comes to event handling, including event bubbling. This means that events triggered inside a portal can bubble up to their ancestors in the React component hierarchy.

To implement event delegation in a React application, you should create separate event listeners for each element. This approach involves attaching a single event listener to a common ancestor and utilizing event propagation to handle events for multiple elements efficiently. It's a common technique to reduce the number of event handlers and optimize performance in large-scale React applications.

Portals are particularly useful in a React application for creating modal dialogs. Portals allow you to render components outside their parent hierarchy, which is essential for modals that need to appear above all other content. They are not typically used for server-side rendering, managing API requests, or styling components.