Do righties use the joystick in the right hand? Or is it British/Aus/Japanese/etc pilots using the shifter in the left hand (taken from right hand drive cars)
Aircrafts with yoke: normally you hold the yoke with the left hand and the throttle with the right hand. If you are in the right seat then it will be the opposite, but traditionally the pilot in command is always seated on the left while the right seat is for the co-pilot (airliners) or for the instructor in training flights.
Planes with stick:
Airbus airliners - same as above i.e. joystick left hand, throttle right hand, unless you are in the co-pilot seat.
Most other aircrafts with a stick, including fighter jets, light aircrafts etc.: joystick right hand, throttle left hand; the joystick can either be on the right side of the pilot, or between legs, in either case you hold it with your right hand since the throttle is on the left.
The other primary control on every aircraft is the rudder, which is always controlled with pedals. Some gaming joysticks can simulate the rudder movements by twisting the joystick on its vertical axis but this is never the case in real life, so if you want realism you will need rudder pedals.
I have to admit that it is slightly better than twisting the stick, but still nowhere near the accuracy of actual rudder pedals.
If you are siting side-by-side in aircraft, most - not all - will have the throttle and related components in the center console, so they aren't duplicated and can be used from both seats. By necessity a pilot in command, seated on the left, will fly with his/her stick in the left hand and right on throttle/everything else. It just happens to be that most civil aircraft cockpits have this configuration. A yoke or side stick can stand in for a center mounted control stick in this configuration and is simply a design factor.
If you are sitting in an aircraft with a single seat operation (i.e., no center console) the throttle will usually be placed somewhere to the left of the pilot, so the controls change - right on the stick and left for the throttle. You'd almost never see anything other than a center stick in this configuration, but there are aircraft with side sticks, like the F-16 and F-22.
There are some exceptions, particularly where side-by-side seating is more specialized and not duplicated. See:
Siai Marchetti SF 260 (notice duplicated throttle on left) : http://tagazous.free.fr/affichage2.php?img=8451
A6 Intruder (Right seat is not a capable of flying aircraft) : https://s-media-cache-ak0.pinimg.com/736x/a1/32/a8/a132a868a...
The right hand is typically on the throttle when taking off and other maneuvers, even when using a yoke.
I think that single seat fighters typically have the throttle on the left and the stick in the center, but I guess it varies.
From a UX perspective, I think one major factor was that the pilot probably not noticed or forgot that stall protection was disabled due to the sensor faults. In normal law (mode) the pilot pulls back fully to get maximum lift - even near stall. Instead of a stick shaker warning, the aircraft just silently calculates a (reduced) elevator output.
In my opinion this is a design flaw even if it's a convenient feature in normal flight, as a confused or stressed out pilot might follow the normal procedure in a bad situation - which will lead to a stall. As happened at least twice.