How exactly is React's Virtual DOM faster?

I have found the answer to my question.

The key is to understand the purpose of the Virtual DOM.

First we have to see what approach React takes to render the components.

Different javascript frameworks take different approaches to detect changes in the data model and render them on the view.

Consider AngularJS. When we refer to our data in an Angular template, for example in an expression like {{foo.x}}, Angular not only renders that data but also creates a watcher for that particular value. Whenever anything happens in our app (click event, HTTP response, timeout), all the watchers are run. If the value in a watcher has changed then that value is re-rendered in the UI. By running all the watchers AngularJS is essentially finding out where it needs to make the changes. The process of running these watchers is called dirty checking.

React takes a different approach. Whenever there is a state change in a React component, instead of finding out where to make the changes (like AngularJS), React re-renders the entire UI from scratch (with the updated state).

But this approach of React has a problem. To re-render the entire UI means to re-render the entire DOM tree. This is a problem because DOM updation is a slow process (due to reflow and repainting).

This is where React's Virtual DOM comes in. A Virtual DOM is just a representation of the Real DOM in form of javascript objects. It is just a tree data structure of plain javascript objects that exists in the memory. As compared to the Real DOM, rendering of the Virtual DOM is much faster because it is never rendered on the screen (no reflow or repainting needs to be done).

So how does the Virtual DOM solve the problem? When we load our app, React creates a Virtual DOM that is an exact virtual copy of the Real DOM. Whenever there is a state change in a component, instead of re-rendering the entire Real DOM, React renders an entire new Virtual DOM (with the updated state). Then it does a diff between the old Virtual DOM (the initial copy of the Real DOM) and this new Virtual DOM (rendered after state change) to find out the changes between them and it does ONLY those changes in the Real DOM. In this way, the entire UI is re-rendered (by rendering an entire new Virtual DOM) but only the minimum required changes are done in the Real DOM.

So when it is said that "Using Virtual DOM React updates only those elements that need to be updated" (point 1 in my question), it means that with the help of Virtual DOM React is overcoming the limitations of its own approach (approach of rendering the entire UI from scratch).

This answer also explains the same concept.

I have seen some answers that state that DOM manipulation using React is faster than using the DOM api because the DOM api re-renders the entire DOM tree whereas React re-renders only those parts of the DOM tree that need to be changed. This is NOT true. All modern browsers are efficient enough to update only those parts of the DOM tree that need to be changed. This can be verified using paint flashing in developer tools of browsers (also see this answer and this answer). Even if we assume that the DOM api does re-render the entire DOM tree, still this reasoning is false because the internal code of React itself has to use the DOM api to update the DOM. If the DOM api did re-render the entire DOM tree then React would also re-render the entire DOM tree because eventually it also uses the DOM api to update the DOM.

 
As for the second point, React actually makes batching easier for us.

In React, while the reads are done on the Real DOM, the writes (state changes) are not done on the Real DOM. Instead the writes are queued. Then when all our reads and writes have been processed, a new Virtual DOM is built based on the writes. Then diffing is done between the old and new Virtual DOM and then React writes the required changes to the Real DOM to update it. Hence eventually all the writes on the Real DOM are done together in a single reflow.

But we can manually also, without React, write our code in such a way that first all reads are done and then all writes are done. React makes batching easier because with React we don't have to care about doing the reads and writes together and React will automatically batch the writes for us. So React does not make things fast. It makes things easier.

 
In conclusion we can say that React is not actually faster. It is easier. As Pete Hunt says in this video, "React is not magic. Just like you can drop into assembler with C and beat the C compiler, you can drop into raw DOM operations and DOM API calls and beat React if you wanted to. However, using C or Java or JavaScript is an order of magnitude performance improvement because you don't have to worry...about the specifics of the platform. With React you can build applications without even thinking about performance and the default state is fast.".

This post by Rich Harris also states that it is a myth that "the Virtual DOM is fast".

Once React knows which virtual DOM objects have changed, then React updates only those objects, in the real DOM. This makes the performance far better when compared to manipulating the real DOM directly. This makes React standout as a high performance JavaScript library.

Regarding the Batch Update:

React follows a batch update mechanism to update the real DOM. Hence, leading to increased performance. This means that updates to the real DOM are sent in batches, instead of sending updates for every single change in state.

The repainting of the UI is the most expensive part, and React efficiently ensures that the real DOM receives only batched updates to repaint the UI.