Yes. Absolutely

That looks like it. But anyway, you can do this without any library, because ReactDom out of the box could mount component to any DomNode.

You can use this interactive lifecycle simulators to learn about it https://reactarmory.com/guides/lifecycle-simulators

redux-saga has a very details testing page here: https://redux-saga.js.org/docs/advanced/Testing.html

I think that's what I would called widget. IMHO, React is a poor choice for such thing because of its size (react + react-dom is about 30 KB last time I check). I usually use preact-habitat to do this

Material UI doesn't use jQuery. And most React.js library try to stay away from jQuery as far as possible. Because jQuery mutates the DOM directly, and React assumes that it's the only one who mutates the DOM. Also, material-ui isn't from Google. The Material Design specs is from Google. material-ui is a library that implements Material Design specs.

All the library you listed above provide common components like Dropdown, title, sidebar, header, ... with default theme so you can create your app quickly. You can write those common components yourself or use libraries. But whatever you choose, choose it wisely. You don't want to fight the libraries to get stuff done.