To be honest, Barrichello isn't someone you should pay that much attention to on such topics. I think he's the only F1 driver that still uses his right foot for braking when it's proven that left foot braking provides a clear advantage.
Also, F1 highly depends on passive safety systems instead of ones that require driver input, because when things go wrong, there usually isn't much a driver can do to fix it anyways.
Do you have a pointer to good info on the left foot braking thing? I wonder if it's applicable to normal driving as well. I remember thinking that right-footed braking seemed dumb when I was learning to drive. The best explanation anyone could give me was that in a panic you might slam on both pedals, which didn't seem like a great argument.
When driving a stick shift, you'll frequently need to shift gears while either accelerating or braking, meaning your left foot must always be free to operate the clutch while the right foot is either on the throttle or the brakes.
If you get into the habit of braking with your left foot while driving an automatic, you'll have real problems whenever the need arises to drive a manual. I think that's a much better reason.
Actually you do want to slam on two pedals, let me explain:
You slam the clutch pedal with the left foot, and the brake pedal with the right foot. While the clutch is pressed, you shift to neutral.
Depending on the speed, you can make the wheels stop rotating while the car is still moving, something that damages the tire. ABS brakes mitigate the risk of this happening.
So the correct technique involves that the strength applied to the brake pedal is more or less proportional to the speed, braking very lightly when the speed is low. This will make the car slow very quickly, in an emergency situation.
Other possibility is when negotiating a corner where you know you don't need to shift speeds. Therefore you can brake a little with the left foot while having the right foot on the throttle and simply accelerating on the corner exit.
This is in contrast with heel toe down-shifting, where you need to use the left foot to control the clutch pedal, and the right foot to control BOTH brake and throttle pedals.
Finally, the nice thing is that you could be doing all three techniques in a single lap in a track.
Left foot braking can be done for very different reasons. First of all, you're probably driving an automatic. It's much trickier to use your left foot to brake when it's also on the clutch. ;)
In the context of F1, it allows for less time between being on the gas and getting on the brakes. Not sure if these are used in F1, but I also remember reading about funky techniques where you can use the gas and brakes at the same time to mess with the balance of the car.
that is not a straight forward question since it depends a lot on the car and how you are driving. for instane, is it an automatic, is it a manual, is it an electrohydraulic with automatic clutch, double clutch, dog-shift gearbox, how responsive is the throttle etc. also, are you driving on a loose surface, tarmac, icy conditions? what does the torque curve of the engine look like (for instance, does your car have a whopping big turbo that has to be kept above a certain RPM to have power on tap?)
in an ordinary car: use your right foot. it is likely that this is what you are used to so your right-foot motor skills (pun intended) will be significantly better. if you have tried to brake with your left foot, and you are not used to it, you have no doubt experienced that you will tend to apply too much brake too quickly. and at the other end: if you have a braking system that takes a lot of force and you have grippy tyres, your left foot will probably significantly weaker as well.
if you want to play around with it a bit I can recommend gokarting. gokarting is brilliant for practicing braking with your left foot as most rental gokarts have crap tyres that are real easy to lock up at even modest brake inputs :)
Also, F1 highly depends on passive safety systems instead of ones that require driver input, because when things go wrong, there usually isn't much a driver can do to fix it anyways.