after connecting my quanum nova to mission planner and starting the initialize setup,
only three of four engines were running.
I heard about the fact, that I shouldn’t update the firmware.
But mission planner installed the latest firmware automatically.
Mission Planner does not update the board firmware automatically. You are probably referring to Mission Planner updating itself.
The Quanum Nova comes with APM:Copter v3.1.2. I have tested this version as well as v3.1.5 and the latest v3.2 which is no longer in beta.
The tlog you posted is recorded by the Mission Planner when you connect your APM to your PC. What would be more helpful is the dataflash log. Use the link here to understand how to download these logs using the Mission Planner’s Flight Data screen.
What exactly did you run in the Initialize Setup section? Note that board firmware cannot be updated from this section. Do all 4 motors run when not connected to Mission Planner?