I have something for number 2:
distance# = 2 * radius * pi * angle#/360.0
<=>
angle#/360.0 = distance# / (2 * radius * pi)
<=>
angle# = 360.0 * distance# / (2 * radius * pi)
<=>
angle# = 180.0 * distance# / (pi * radius)
So to calculate the angle when turning to the right:
TheCarsAngle# = TheCarsAngle# + (180.0*speed#/(pi*radius)
And to the left:
TheCarsAngle# = TheCarsAngle# - (180.0*speed#/(pi*radius)
(I hope I didn't calculate something wrong...)
note: pi = 3.1415926543 (and so on) and radius is the distance to the center. The bigger it is, the bigger it's turns.
note 2: This is NOT slipping.
It's the programmer's life:
Have a problem, solve the problem, and have a new problem to solve.