After reading the manual again, which also states that you can use the mouse, I remembered that I have to press the "F10"-key to jump into firing mode. Stupid me...
So the 3.point is a resolution problem of the warthog throttle.
So this one is solved, that only leaves the other 2 as key mapping problems.
Is there a way to invert the Y-axis of the mouse for the gunner? It drives me nuts to scroll down, when I want the MG to move up.