Hi!
1. I know what Boxer means by saying 'neutral' position, but looking at your question, I have to deny this. The knob itself always stays where it is, it never stays in or our. If you push, you're in manged mode, if you pull, it's selected mode.
Pull on the knob and you see the current speed displayed in the FCU window and the airspeed indicator shows you a blue little arrow/ triangle. Push the button and the numbers in the FCU window disappear, a white dot shows up and the symbol on the PFD turns magents and moves to the managed speed calculated for the phase of flight: managed mode. If you just turn the speed knob without pushing or pulling, it shows the current speed. You can now go, select a speed and when you're ready, you pull and this becomes your selected speed. If you don't pull, this number will disappear after maybe 30 secs and the dashes reappear since you're still in the managed mode. You can pre-select some speeds in the MCDU during preflight. If you want a managed climb speed, as calculated by the FMGC per cost index etc but you want a constant M.80 cruise speed, you just enter this into the PERF page for cruise (anytime before the mode becomes active) and when you reach cruise altitude, the FCU window shows .80 (mach) AND the white dot, indicating that even though you told it what speed to fly, it is still in the managed mode. It manages speed now with your preset speed instead of its own calculated. But: either managed mode or selected, nothing in between, no situation not being in either mode.
2. Vls is the minimum maneuvering speed for the current configuration. You will find two different Vls speeds on the plane. One is on the PERF APPR page in the MCDU. This is a static number and is calculated as Vref for landing using Flaps FULL (unless you tell the box to use Config 3).This provides 1.23 Vs protection . Then there is Vls as it shows up on the PFD airspeed tape. This constantly varies according to the current configuration and flight condition.
It is the minimum speed the airplane will fly with the autoflight system on. If it's e.g. 140 kts and you select a speed of 120 kts, the autoflight system will slow to 140 kts and stay there. In itself, Vls has nothing to do with Alpha Prot or Alpha max.
3. First, when you think max continous, think engine failure. You don't use it for normal flight. The detent is called FLEX/MCT, which means that during normal ops, it provides FLEX power as long as there is a FLEX temp entered on the PERF page and it is higher than the current TAT. If one engine fails, the airplane thinks differently now and the same setting now provides MCT as soon as you reach the acceleration altitude during climb. If there is no FLEX temp entered or if the FLEX temp is equal to or lower than the current TAT, the ECAM will tell you use TOGA if you set the thottles to the FLEX/MCT detent during take-off.
4. I'm not really sure what you're asking here. The GS and LOC act like any other airplanes receivers. They do false captures etc. like on any other airplane, no difference there, let me know if there is something specific , related to the FMGC etc. that you're looking for.