That's right transmissions are separate from engines, so they must have their fluids replaced as much as possible. A transmission flush may not be a wise choice as it is performed under pressure. Undue pressure may dislodge O-Rings, and seals, which may cause your transmission to lock up. There have been many cases where the vehicle dis not move after a transmission flush.
A drain and fill is safer, but it only drains about 50% of the old fluid because the rest of it sits in the torque convertor. Some people will lift/tilt the vehicle towards one side, and leave it overnight so as to allow the torque convertor to drain. This may yield another quart or so. After replacing the filter, and pan gasket, fill it up. You may now have 60% new fluid. Most people understand/accept this predicament. To fully drain the entire fluid requires transmission R & R ($1500). We live in an imperfect world :(
Yes. The fuel used in the engine has nothing to do with the transmission. Your owner's manual will give you the interval for the recommenced transmission fluid change.
Regardless of the fuel used in the engine, the transmission fluid should be changed every 30k miles, flushing it isn't completely necessary, I would opt for a fluid change instead of a flush.
Just change your fluid. Do not drain your torque convertor unless you plan to refill it with it off the car ,
does CNG cars need transmission flush?