Jeps, all stock brakes are sufficient. There are laws for this. Once you look at brakes as heatsinks, it starts to make sense.
Driving 4 Answers has some good videos about it
Yes and no.
Talking generally here - The genuine stock brakes are sufficient upto a point, but the legal type approval requirement for braking is really quite easy to pass with a max speed of 160km/h - so the 'law' is a very low bar.
AMS and Vmax brake testing is much more demanding on the braking system, which most OEM's also perform - not due to legal requirement - but due to pressure from road testing magazines.
Looking at discs as heat sink's is really only applicable for multiple stops - for one off 'emergency' stop its all about your pad friction material maintaining a certain friction coefficient. From a high speed stop you can easily get scenarios where the friction coefficient drops enough due to heat where it doesn't have enough brake torque to enable ABS modulation. A bigger disc will absolutely
help in this scenario as the larger radius provides the same brake torque (and deceleration) for less clamping force which results in less chance the pad friction coefficient drops below the ABS threshold point.
I have conducted brake testing and some of the brands of aftermarket pads we were testing failed to be able to activate ABS as the friction coefficient drops so much in stop due to the heat - the feeling as a driver is really unnerving. This was high speed and GVW so quite severe testing but still..
As I mentioned though, the OP should be honest with their expected usage as on a road car you likely won't see enough speed/repeated braking to cause a
problem which needs fixing. Any track use then all bets are off.