To the best of my knowledge, limited as that is, the Null Zone settings for pitch and roll should be almost full left, and Sensitivity, full right, or very close to. That's where I keep mine set. You can have the rudder Null Zone a hair or three farther right, as it's just human nature to not be able to hold your hand perfectly still in yaw as you make inputs to the other two axes. Just a note.
Remember, the FLAPS switch in the cockpit is eye-candy only. It has no effect on the plane. It moves, but doesn't do anything. Personally, I use F5-F8 to operate the Flaps. Essentially, F5 is equal to UP/AUTO, F7 is FLAPS HALF, and F8 is FLAPS FULL. I hit F7 for takeoff only, and upon acceleration above about 240KIAS, I hit F5, to make sure the Flaps are in UP/AUTO. Or, as I am coming up off the runway, I put the gear up, and hit F5 immediately.
For landing, at 250KIAS, slowing down, I hit F8 when I put the gear down, and let the FCS control the flap extension, as it's designed to, as the plane slows to approach speed. The rest of the time, whatever my speed, or AOA, or maneuver, I leave them in UP/AUTO. If I'm not sure, I hit F5 just to be certain.
Do you have FSUIPC Payware version? If you only use the freeware version, ignore this, but if you use the payware version, does it adjust the pitch axis input from the joystick? If so, I would set it to default, so it doesn't modify the input in any way. Be careful, the settings can seem to change on their own, sometimes, so if you have the payware version, definately check all 3 axes. Like I said, if you only use the freeware version, as I do, ignore all of this
I trust you DO vae FSUIPC installed? The latest version? I can go check what the version number should be if you want.
When you look in the VC at the stick, and you let go of your controller, watch the checklist display on the MFD immediately in front of the stick. It has, at the very bottom left the control surface position. Does that return to 0 what ever the stick does? Is there any trim indication on the bottom right, and does IT change at all during all this, without you commanding it, anyway? You can also call up the SHFT+8 page, and on to top right area it has the control inputs the plane is receiving. You can monitor the joystick inputs and see if they match what the plane is really doing.
I am sure it's something in your controller setups, calibrations, the game settings, your FSX.cfg, something along those lines. We will find it!
Pat☺