1) The level of deformation in the tyre is certainly one way the tyre "knows" how much it is slipping, the same as for slip angles.
Below is a good source showing typical force curves for tyres:
http://www.racer.nl/reference/pacejka.htm
The physics of tyres still isn't fully understood, hence why the Pacejka model is called a "magic formula", but empirical data through rig testing and vehicle testing is fairly comprehensive.
2) The graphs shown in the source above are typical of almost all tyres. This is the type of information the tyre manufacturers sometimes supply and are derived from testing on a rig. Sure, temperature alters the shape and where the peaks are on the curves, as do other factors, but the curves are instantaneous for prevailing conditions.
You don't sense the reduced rotation rate, you can feel the increased decceleration rate, you can feel the tyre gripping and ungripping, you can hear when the tyre has lost it's grip (it's much quieter). There are lots of cues drivers use. The rapid drop after the peak is what most drivers sense as a lockup and they very quickly back away from this and build back up to it.
When dealing with the less intelligent drivers you will often hear them claim that a car speeds up after they lose control. We know this is not the case, but it feels like it to them because the rate of decceleration falls considerably.
Regarding the Scandavian flick, there's nothing unusual about it at all. The right hand flick unloads the right hand tyres allowing the kart to change attitude very quickly when flicking back the other way, setting the kart up for the corner without having to steer it (in the normal sense of steering).
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