Question

Ok

why would it be necessary for someone to measure oscillations from a 20 cm mark of a suspended ruler as oppose to the center of mass?

Answer 1

If you suspended it from the middle, the period would be infinite because the rule would balance and their would be no torque to pull it back into a vertical position when displaced. They just hung the ruler from the 20 cm mark to make it more fun than hanging from the end. It makes it harder to compute the moment of inertia.