I like to change all fluids fairly often - like every 2-3 years for light duty/low mileage use. Not sure it really needs it, but it makes me feel better.
The transmission calls for Mercon auto trans fluid. Unless you're racing and need additional heat protection, there's no advantage to using anything else.
The rear diff is a lot like the engine. The fluid you need depends on the use. High heat and heavy duty use (racing) requires
synthetic fluids with a higher viscosity. Light duty use has no need for the expensive
synthetic, and should use a lighter weight fluid.
A clutch type LSD needs a friction modifier.