Yes
Yes
Yes
Yes
Bigger Brakes = Better braking
No

The biggest issue is not a false sense of security, it's understanding how AWD works and using it to the fullest. The gut instint people have when their car begins to skid is to lift off the gas and smash the brakes.
If you think about it though, the best thing you can do is continue to add gradual steady pressure to the accelerator, this way the front wheels are pulling you and the rear wheels are pushing you and you have increased traction. By jamming the brakes, the AWD does little to nothing.

So remember, the next time your car starts to skid, keep your eyes focused on where you want the car to be.. NOT THE WALL COMING UP AT YOU. If you stare at the wall, you will hit the wall. If you stare at the area of "safety" your hands will follow your eyes to the "safety" area. This in conjunction with not unsettling the weight distribution of the vehicle and keeping nice smooth pressure on the gas should be your best way out of a sticky slide.

-- Just because you have something like AWD does not mean it works all by itself, you have to help it by making the right decisions which can sometimes be counter intuitive.

B

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"When two people agree on everything, one of them is not necessary" - Arliss