Hello! I can't say 100% about what you are talking about as I have never touched a Hybrid CrossFire setup before but from what I have experienced with regular CrossFire X and what I have read about Hybrid CrossFire I can say the following...
Is it possible with that combination to connect my display to the APU and having the HD7850 in the enrgy efficent ZeroCore mode?
Yes, you will connect your Monitor to the motherboard's graphics port, so it will primarily use your APU graphics until you start a 3D application.
And is it possible to use the HD7850 while the display is still connected to the APU?
If you plug in a monitor to the 7850 it will automatically disable CrossFire but can still be used.
Is it possible to activate the HD7850 while some 3d app is running?
Yes, CrossFire X will automatically start when a 3D application is ran and as long as that application and AMD's software both support CrossFire X code.
Ultimately, you will need to refer to your motherboard manual for more concrete answers.
The opinions expressed above do not represent those of Advanced Micro Devices or any of their affiliates.
Requiescat In Pace AMD Processor Forums | Member since: 1/19/2009 | Post count: 4142
Please don't PM me with questions, instead create a thread so that everyone can assist and benefit from the knowledge provided. Thanks in advance!