What is the most common stair tread depth and stair nosing length?
I doubt any of us can provide actual statistics. You'll get personal preference and opinion. Mine is to shoot for 1-1/8", knowing that cutting stair stringers takes precision and still results in a bit of variation after all is said and done.

Tread depth does include the nosing. "Run" is the term for each step's dimension from riser to riser. "Rise" is the dimension from tread to tread.

______________________    __ 
______________________)    ^
                   ||      |
                   ||      |
                   ||      | rise
                   ||      |
                   _______________________
                   _______________________)
                                       ||
                    |
                    |&lt;--- run ----------&gt;