Teach The Cat to Shit in the Toilet

That's phase 2! Quit rushing ahead.

You could achieve the cat flushing action via something like an Arduino with a servo motor and a little creativity in which the cat touches a sensor after using the toilet and it causes the motor to turn which is connected to the jig in the back of the toilet that pulls up that plunger thing and flush the toilet. Just use some Pavlovian classical conditioning to get the cat to touch the sensor and presto cat shits in toilet!