Purpose of Nonclustered indexes in SQL Server 2012
You've got two questions in here:

1. Does the nonclustered index have a sorted B-tree? Yes, because you have to get to the right page of the index to find the data you're looking for.

2. Why do you want a nonclustered index when you also have a clustered index? Think of the white pages of the phone book as your clustered index. If you wanted to find all of the people in your city with a first name of "Brent", then the clustered index isn't going to do you much good - the clustered index is based on last name, first name, middle initial. Wouldn't it be helpful to have a separate phone book sorted by first name?

Just like in real life, the answer to that might be yes or no - but it depends on how often you search for people by first name, and how often people move in/out of your city, or how often people change names.