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This can be understood in terms of vector differentiation and the dot product. Take the example that $v \perp r$. The change in the square of the displacement is $$\frac{d}{dt}r^2$$ $$=2r \cdot v$$, and if they are perpendicular, the dot product is zero.

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Laser Doppler velocimetry can be used. Generally it is used to measure velocity of this range for any transparent fluid flow.

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If you're both going at a constant speed, lets say 35 MPH, then it would appear so. This is because the distance is shorter in the inner arc in which you are traveling compared to the outer arc in which the other vehicle is traveling.

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Here we are talking about instantaneous velocity. So,its -20 m/s. And the velocity will be always tangent to the circular track. So,it will be 20 m/s in magnitude every second. But the direction will be different so different values in x & y - axes

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