Does creating an account reset your progress?
According to this Wikia page, it's just a way to share your score and progress, you should not suffer any reset (or restart, as you call it).
No, it won't. It will keep your icon, it will only change your unregistered name to your account name. :) you should most definetly make one, because that's the only way you can send messages to other people, friend other people, etc.