The question with cursor is already solved, I don't need positioning it to the center any more...
And about rotation, I don't know why but tilt does not perform as a local rotation...Here is a sequence of screenshots for more detail:
1. all angles = 0

2. Change the tilt angle , the plane goes upward.

3. Roll the plane a little to the left

4. But when I tilt it again the plane still goes upward (solid arrows) instead of rotating along its local coordinates (dashed arrows)

Here's the code I'm using:
var rotation_coef = 10;
...
action()
while(1){
...
if (key_w) { player.tilt -= rotation_coef * time_step;}
if (key_s) { player.tilt += rotation_coef * time_step;}
if (key_a) { player.roll -= rotation_coef * time_step;}
if (key_d) { player.tilt += rotation_coef * time_step;}
wait(1);
....
}
Any ideas why ithis happens?