Such apps should be rated as Broken. However, it’s essential to mention in the Notes indicating that these apps rely on Play Services during the first launch but continue functioning even if Play Services are uninstalled afterwards.

Yes.

Sure, developers are welcome to include their own apps for rating.

This is because having an app installed mostly implies active usage. While installation alone doesn’t guarantee usage, it’s a reasonable assumption that users can provide feedback on features they’ve interacted with.