The render() method is the required method to be defined for a class component in React. This method is responsible for rendering the component and returning the resulting element tree. All other methods, such as constructor() and componentDidMount(), are optional and serve specific purposes in the component lifecycle.

React Router is a higher-level abstraction on top of the history library. It provides a declarative API for routing and navigation in React applications, and manages the browser history and URL updates. The history library, on the other hand, is a low-level library that provides a simple interface for manipulating the browser history, and can be used directly in non-React applications.

Hooks in React can replace both render props and higher order components in some cases. Hooks can provide similar functionality to both of these patterns, while also simplifying the code and making it more reusable. For example, the "useEffect" Hook can replace the "componentDidMount" and "componentDidUpdate" lifecycle methods, as well as some uses of higher order components.

React-Intl is a library for internationalization (i18n) in React applications. It provides a set of components, utilities, and formatting functions to handle different languages, locales, and cultural conventions. With React-Intl, you can easily translate text, format dates and numbers, and manage pluralization and gender.

In React, there are several rules for naming components, including that components must start with a capital letter, use camelCase convention, and can include numbers, but not as the first character. Components should also have a descriptive name that reflects their purpose or function in the application.

The recommended ordering of methods in a React component class is as follows: constructor, render, lifecycle methods, event handlers. This ordering groups related methods together and makes it easier to understand and maintain the code.

In React, you can programmatically trigger a click event by using the "simulate()" method in the "react-test-renderer" package. This method allows you to simulate a click event on a React component, and can be useful for testing or automation purposes. For example: TestRenderer.act(() => { buttonInstance.simulate('click'); });.

React Dev Tools is a browser extension and development tool that provides a visual interface for debugging and inspecting the state of a React application. It allows you to track and debug the state and props of your components, as well as inspect the component tree and the performance of your application. React Dev Tools is available for Chrome, Firefox, and other major browsers.

In React, you can make an AJAX call by using the "fetch" API or a library like Axios or jQuery. The recommended lifecycle method to make an AJAX call is "componentDidMount()", which is called once the component has been mounted to the DOM. This method is a good place to fetch data from an API or server, and update the component state with the new data.

Relay is a library for handling data fetching and caching in React applications. It is often used in conjunction with GraphQL APIs. While Redux is a state management library, Relay focuses specifically on data fetching and caching. Relay provides a number of features, such as declarative data requirements, automatic query generation, and optimistic updates.