SQL Server 2008 R2 - Service shutdown - what with running stored procedures?
When I go to the services.msc and stop the SQL Server, the service
  will be in 'Stopping' state until @ScheduledProcedure is completed
  (8-10 mins).


What you are seeing is the default behavior when you shut down SQL Server. If you do not want want to wait you can use WITH NOWAIT switch but when SQL server starts recovery time will be longer as transactions has to roll forward and roll back.

Details here.

Unless the WITHNOWAIT option is used, SHUTDOWN shuts down SQL Server by:


Disabling logins (except for members of the sysadmin and serveradmin
fixed server roles).
Waiting for currently running Transact-SQL statements or stored
procedures to finish. To display a list of all active processes and
locks, run sp_who and sp_lock, respectively.
Inserting a checkpoint in every database.
Using the SHUTDOWN statement minimizes the amount of automatic
recovery work needed when members of the sysadmin fixed server role
restart SQL Server.



  When I shut the OS down it seems that SQL Service cancels stored
  procedure. I think that it is the case, because Stage 2 and 3 messages
  are not available in test_log table.


In this case SQL Server has no control as operating system issue a shut down process command and that is why you are seeing immediate shutdown.Transactions that were completed and written to the transaction log but not yet applied to the database, will be applied to the database. Open, unfinished, transactions are rolled back, again to ensure the database is in a consistent state.  Details about roll forward and roll back here.

Different ways to shut down SQL Server.