I was told that you should not select the auto mode on the centre console when driving it manually until the car is completely stopped. Is this correct?
I"m not sure why you'd ever want to use auto mode, but if I were to select it, it would be from a stop. You can change the manettino on the fly.
Not correct. You can select auto mode at any time, moving or stopped. To deselect simply pull one of the paddles or push the button again at any time. Most of us don't use auto mode much but it's very handy when the SO (or other incomp) wants to drive but doesn't want to deal with shifting. Contrary to popular internet myth, F1 auto mode has no appreciable affect on clutch life since it uses same software as normal mode paddles.
With the 599, you can push the Auto button and the transmission goes into auto mode. To get it back to manual mode, you need to push and hold the Auto button. Is the same case for the F430, or will a simple push-and-release suffice?
Push and release is sufficient, or using either the up or down paddle. I use the down paddle most times.
In the Scuderia, it starts in Auto mode, but by shifting a gear with the paddles, it will take it out of Auto mode. I was told this was their way to deal with the average MPG issue. I would imagine you do get pretty good mileage (relatively speaking) if you shift at 3500 RPM, but I haven't driven it long enough in Auto to test that hypothesis.