Ok, after clicking DEFAULT MAP, your X, Y and Z axis should be mapped like this:
Relog after mapping those analog inputs, for AH to actually recognise them. Then you can check if the axis are assigned correctly by moving your stick. That should make the numbers in brackets of the corresponding axis change (ie if you move your stick left and right, your X axis (analog input ROLL) should be changing). Dont forget calibration in game.
X/Y rotation are probably the rotaries. You can map those to Trim manually if you like (as you can see in the above picture, i have my Rotary1 mapped to elevator trim) - but id say use combat trim for the time being, you still have a lot other things to worry about
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slider and move up/down/left/right are slider levers on your JS or Throttle you can assign for example to zoom in or move your head around. But to be honest, same as for trim.... dont worry about that yet. If you have your views and head positions set up, youre doing fine... no need to worry about another slider/button in fight.
PS: If your stick is still very touchy after calibration, try scaling it:
Youll have to do this for each axis - mainly X and Y, seperatly - check the ADVANCED box to get the window. The setting shown is one where you can start from. Adjust from there, as you feel you need to. The higher the slider, the more instant the reaction to input. if you want it a bit less touchy, lower the staircase and/or add a bit damping. Dont let your controls get too sluggish though.