Why did the Concorde require a droop nose and how did it work?
1) Though already mentioned that this might be too broad, I would dare to guess a properly fitted camera could do the trick. But I doubt that this would be effective considering the technology of the era that Concorde was developed.

2) Concorde due to its design for supersonic speeds, it was generating too little lift at low speeds (like those needed for landing). So they had to take into advantage another way of producing lift: vortex lift. In order to produce vortex lift, you need relatively high angles of attack and consequently high pitch attitude.

3) I cannot answer this since I am not an engineer. Though with little googling I found this. It seems to be very detailed, with photos of the lever and diagrams of the mechanism.