I use the monitor cab off function and run into a Matrix 1600 then into a Mesa 4x12 works great. I dont want to turn the cab off because that is used to feed the FOH. Right now I am a big fan of OwnHammer IR's. So I just match the IR to what I hear coming from my cab and go with it live.
When using a real cab I turn off the Profiler's cab 100% of the time.
Only for acoustic sounds.
Yes. Monitor cab off.
Yes- I turn it off so I don't color the Marshall 1960a Cab tone I am playing thru.
Definitely cab sim off. Using it removes all top end life, methinks. I use monitor eq to adjust for frequency response that I may find lacking or too pronounced in the cab.
I've tried some real cabs where keeping Cabinet on made them sound definitely better to my ears.
Yes As always, it depends on the pair of ears you are using. But I sometimes don't trust them. 
