Let me give a try.

I may need to be quite picky with terminology, in order not to confuse one thing for another.
When you are at level and you decrease the speed, if it reaches alpha protection, the plane will pitch down to get back speed.
Rephrase needed: If you fly level and select thrust idle, the aircraft will initially maintain altitude but obviously deccelerate. Once the speed gets as low as V alpha prot (the top of the amber band), the alpha protection activates and will pitch nose down as necessary to maintain this Valphaprot.
QUESTIONS AT LEVEL
1) At which speed will it fly? The upper limit of Alpha protection?
2) But what if you had entered a speed in the FCU, and that speed was bellow VLS, will the plane maintain that speed or the alpha protection one?
3) The plane will go down, but what happens if you had your altitude managed?
4)Will "that" speed be managed by pitch?
1) Yes, see above.
2) Forget VLS this time, that's for Autothrust. We assume A/THR is off.
3) in my scenario, as the aircraft is not able to maintan level due too little thrust, the activation of alpha prot (nose down command) will disregardt the "ALT HOLD".
4) Yes, the aircraft will pitch up or down to maintaint V alphaprot.
- When you pull your stick, the plane will reach Alpha max, but Alpha floor will give max TOGA, till we leave the stick where alpha protection will pitch down and maintain the upper speed of alpha protection.
Fair. Note that TOGA is commanded by the A.FLOOR feature, the max thrust will remain selected irrespective of stick position.
QUESTIONS GOING UP:
1) If we have climbed, I imagine that our altitude was not managed, or not even selected (open climb), the altitude function has disconnected, am I right? If yes, no questions about altitude!
1) Same question, will it maintain that speed by pitch?
2) What if we had entered a speed in the FCU? Will it still fly that one?
1) Your use of words "managed" and "selected" seem to indicate a different meaning to them compared to what I am used to. But my example assumes no altitude functions connected in a first place.

1) Yes, the alpha prot function, unless overriden by push/pull on the stick, will always adjust pitch so that aircraft will not fly slower than Valpha prot (top of the amber band). This may cause increase of descent (e.g. with thrust at idle), or a reduction in climb (e.g. with TOGA). The resulting trajectory will always depend on how much thrust is available from the engines in any particular moment.
2) See above, FCU speed selection is for guidance modes of autopilot and/or autothrust. I assume none are used.
QUESTIONS WITH AN EXAMPLE
We are flying A320 and here are our waypoints:
-AGOPA: FL80- 220 knots
-LORNI: FL60- 210 knots
-MOPAR: FL50- 205 knots
-MANOX: FL30- 180 knots
We are at AGOPA, FL80 entered in the FCU, speed managed.
We forget do enter FL29 managed in the FCU, speed reaches 185 knots, and hits alpha protection and pitch goes down to regain speed...
1) At which speed will the plane fly?
2) Will it then leave our managed speed? Or still try to reach it?
3) At which altitude will it stabilize? Will it leave the managed altitude?
From my point of view, the example you give involves interaction of speed protection function with altitude guidance, speed orders and, more over, the flight navigation computer's vertical features. To explain properly, we'll end up writing full FCOM. I'll need to pass.

Still
2) see above. The alpha prot will, at any time, reduce the pitch so that speed never goes below Valpha prot (top of amber band). Irrespective of any FCU or FMS settings. The only way to
not pitch down is to pull on the stick, and override alpha prot. Then the speed would most likely drop all the way to V aplha max (top of the red band) at which point the alpha max protection will reduce the pitch to maintain V aplha max. This cannot be overriden.
3) Unless some action is taken, the unavoidable final altitude will be AGL=0. (joke, but true).
EXTRA QUESTIONS
I just would like a approximative number for these questions: (A320- A330)
1) What is generally a take-off angle?
2) A climb angle?
3) A cruise angle?
See what I read!
"Pitch during descent is only slighty negative e.g. at low altitude (e.g. 5000ft) at 64500kgs and 250kts the rate of descent is 1660ft/min which results in a pitch attitude of -0.6deg
At 214kts (approx green dot) the pitch attitude is +2.3deg during an idle descent!"
4) A descent angle?
5) After green dot angle?
6) Rotation altitude?
I assume by "angle" you mean pitch. My best guess for A320:
1) 13-18 deg nose up. Depends on speed / weight.
2) 3 to 12 deg nose up. Depends on speed / weight / altitude.
3) 1,5 to 3 deg nose up. Depends on speed / weight / altitude.
4) 3 deg up to 4 deg nose down. Depends on speed / weight / altitude.
5) Question not understood.
6) Likewise.
EXTRA QUESTIONS PART 2
1) Why during take-off the Alpha protection and alpha max is equal for 5 seconds?
That is the way the software is designed. Probably to allow for dynamics of takeoff itself.
QUESTION WITH A SADLY CRASH:
1) Why did AF447 stall? Didn't alpha floor react? Or was it too late?
Very simplified: The sensors were providing erratic information. In such case, the protections were de-activated by internal logic.
Take care,
FD.