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yes you are right. and that uncertainty is due to the effect of the fringe capacitance.
nowadays, there is formula for getting the actual value of the capacitor and fringe capacitance is already included in the calculation.
No - the reason to maximize the perimeter has to do with the fact that fringing capacitance is proportional to perimeter of the cap. When we model a parallel plate cap, we disregard the fringing capacitance and say that all of the capacitance is due to the area. We can't make this assumption when there is a large perimeter.
Look up Hajimiri & Lee's paper of lateral flux capacitors (fractal capacitors) for more information.
As far as mismatch / uncertainty goes, Pelgram shows that the variance of capacitance is inversely proportional to cap area.