You should leave the ./index.js entrypoint file as it is otherwise you may run into an issue when it comes to bundling a production build.
Run yarn tsc to type-check your new TypeScript files.
How TypeScript and React Native works
What does React Native + TypeScript look like
You can provide an interface for a React Component's Props and State via React.Component<Props, State> which will provide type-checking and editor auto-completing when working with that component in JSX.
[React + TypeScript Cheatsheets][cheats] has a good overview on how to use React with TypeScript
Using Custom Path Aliases with TypeScript
To use custom path aliases with TypeScript, you need to set the path aliases to work from both Babel and TypeScript. Here's how:
Edit your tsconfig.json to have your custom path mappings. Set anything in the root of src to be available with no preceding path reference, and allow any test file to be accessed by using test/File.tsx: