In Settings -> Buttons, I can assign a program to "Button 3 (Press and Hold)" but I don't see on the list "Button 3" (without holding, like for the others). How come?!?

Because HTC (the maker of the 6700) didn't program the button driver to have that option.

If you want more sophisticated control of all of your phones buttons I suggest an app called AEButtonPlus. You should be able to pull it up with a google search.

ummm ... that's because a single press of button three is hard dedicated to taking a picture.

If you assigned something else to it you wouldn't be able to take any pictures once the camera application was running.