You can specify different exports based on environment in the package.json so you could ship TS files… alongside JS files, so it feels a little redundant.
Yes, I recommend shipping TS source alongside compiled JS+d.ts even if you don't support a TS native environment, because you then have the potential of a source mapped debugging experience within that library (though currently doing that is a bit painful in some debuggers).
Of course. A few more kilobytes is a good tradeoff for debuggability and the ability to read the original code during development. Web apps that get bundled won't include it, ESM web apps won't request them, and if a server side application is sensitive to deployment size, it's trivial to remove source files from all dependencies during build. As an application developer I'd much rather an upstream package provide it and let me strip it out than the opposite.