You can integrate the React application with some back end language?
React is just a way to manipulate front-end, then all you can do in the front-end is available when you use React, including accessing back-end. In fact he has some facilities to work better with what comes from back-end and how to send to him.
If that’s what you’re talking about integrating, then yes. If you’re talking about using React on back-end, I would say yes, but it is a little different, it is possible to take advantage parts. This is a technique isomorphic and can be obtained more easily with tools such as Redux. You can see more in one article. And a example. And another.
I can apply React to small projects or only when needed?
Power always can, but needs to analyze if it should. I would avoid heavy things like React for small and simple things, but it depends on the goal. I have a tendency not to use frameworks unless you prove yourself very useful, and tend to use something lighter like the Vue.js until you need something more complete.
React is just a tool of what you are describing about SPA.
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– Maniero