Now we are getting close!
"Do you mean that in climb mode, AP/FD has to manage and control the speed? I had thought that A/THR will send to the AP/FD the pitch the plane should have...Do you mean that in this case, FM will send the pitch the plane should have to manage the speed??? So basically FM is managing the speed?"
Exactly! Thrust is fixed at Climb power, AP/FD control pitch to keep the speed.
Example 1: This goes back to the question that I am not sure of.
As soon as the protection disengages, it will keep 175kt (controlled by the A/thr, in SPEED mode). Before the protection disengages, I am not sure.
Remember to disengage the protection you have to: Push the stick Greater than 8 ° forward, or,‐Greater than 0.5 °for at least 0.5 s when α < α MAX.
Example 2: Maintains 130kt with no sidestick input.