Tom has already answered the important points. I just like to cover the last question:
If the answer to question 1 is yes, then what is the use of being able to add a database user / group from a domain?
Keep in mind that a user can have access to the instance from one or more AD groups. But then the user or an AD group may need specific permissions in a database, and therefore you may need to add the user on this level, although the user has no login of its own.