Re: Mechanchim embarrassing talmidim,please read Chaim Walder’s People Speak #4.A few of those stories are on that topic and really drive the point home.
Re:giving someone mussar,it is always best to take the person aside.
As far as the exact loshon:that causing a person’s face to turn white (with embarrassment) is as if he killed him…I watched a parent pass away,and that is exactly what happens…so likening boosha to misa is not an exaggeration.