You are correct, React in itself as a smaller scope than Angular, it is not a so-called "framework" but it's a library used to render views, or components inside a view. You will have to assemble many other libraries around React to get a full SPA application, however the good news is that skilled developers already picked them for you and pulled out very useful boiler plates that should get you started much much faster than if you were to do all the work by yourself.
Take a look at those:
Find your perfect React starter project
react-boilerplate
react-redux-starter-kit
I based my latest app on the 3rd one and I love it, but it's personal ...
Now your questions:
Yes you can use both, take a look at ngReact, let's you run React components in an Angular app. If you start from scratch however and don't have legacy code or libs written in one of the two technologies, my recommendation would be to either use one or the other. This kind of hybrid solution would let you slowly migrate an Angular app to React by rewritting one by one your components without breaking the whole app at once.
That's pretty much what I said in 1/ this can be done but if I were to write the app from scratch I would pick either Angular or React depending on time constraints, existing code base and willingness to learn a new framework. My recommendation: take a few days to experience various boilerplates and pick the one that you feel the most comfortable with...