All of these questions and more are what neurolinguistics is about. We can see more and more accurate traces of our electrical brain waves and understand more about how they reflect our responses to statements that are true or false, ungrammatical or nonsense, and how the brain's electrical activity varies depending on whether we are listening to nouns or verbs, words about colors, or words about numbers. New information about neurolinguistics is regularly covered in national news sources.
Brain activity is like the activity of a huge city.
A city is organized so that people who live in it can get what they need to live on, but you can't say that a complex activity, like manufacturing a product, is 'in' one place. Raw materials have to arrive, subcontractors are needed, the product must be shipped out in various directions. It's the same with our brains. But we can say that listening, understanding, talking, and reading each involve activities in certain parts of the brain much more than other parts. Most of these parts are in the left side of your brain, the left hemisphere, regardless of what language you read and how it is written.