Hi AF330,
it works like this.
You fly level, with stick released, and set throttles to idle. The aircraft will start decelerating toward speed Valpha prot (the yellow band). At Vaprot the low speed protection activates, and in order not to go any slower, the aircraft will pitch down to maintain Vaprot.
If you then pull on the stick and raise the nose, the speed will decay down to V alpha max (the red band). This means you will override the AlphaProt logic and fly slower than V alpha prot. The aircraft will keep descending, as you do not have a sufficient thrust to maintain level flight, but at speed V aplha max.
Actually, no. Because you asked for the aircraft to go upwards with your side stick command, a few moments before reaching V alpha max the A/THR system will command full thrust, irrespective of throttle levers position. This is called the A.FLOOR function of the autothrust system. Unless it is disabled beforehand by a specific trick, it will give you full power from the engines anytime the speeds gets too low (just above Valpha max).
So, eventually you will be climbing after all, with TOGA thrust and at speed V alpha max - provided you keep pulling on the stick. If you release the stick then, your override of AlphaProt function will cease to exist, and the AlphaProt function will lower the nose just a little in order to accelerate twards Valphaprot (the top of yellow band). When Valpha prot is regained, with released stick the aircraft will keep this speed, whilst climbing. The climb is the result of excess energy provided by the TOGA thrust from the engines.
I know this does not really answer all the questions you asked, but I would like to suggest you digest the above first, before going any deeper.
Sounds good?
Cheers,
FD.