The app uses app-specific permissions, and doesn't grant the app access to any data for your other apps or accounts. You can either authenticate with Google if you have an account you'd like to use (it only gives the app access to your email address to log you in.
If you don't want to use your google account, you can register with your email address and a password of your choosing. Again, it doesn't use this for anything other than to store your crews and app preferences to the cloud, so that if you log in with another device or uninstall/reinstall, it'll retain all your stuff.
For the network game you created, it will only show a "Waiting..." message until you generate the little sharing code and send it to another player. When they go to join the game from the Games screen (by pressing the + icon and then "Join", and typing in the code you sent), it will update both of your devices and keep you together in the faction/leader/crew/scheme selection process.