Yes to all.
Stop all BES Services running on BES and BAS.
Backup and restore the SQL databases to the new SQL Server.
Run the setup.exe on BAS to point BMSStore to the new SQL Server.
All your settings should stay intact.
By the way, the Monitoring Service is crap. They heard the howl of dismay from BES Admins worldwide and said to themselves, "Yep, we screwed up again. Let's ditch it!" Hence the reason that BlackBerry ended support for it Feb 20, 2012.
Check it out for yourself: BlackBerry LifeCycle