Re. exercise 3, Homo economicus will in general work more hours, as working has now become more valuable relative to other uses of her time. In reality, as you say, anything could happen, depending on the individual's utility function for money.

Re. number 6, I've taken too many DEs classes to be excited by this problem, but in general a critically damped system will recover optimally from perturbations.

Re. number 7, one good way is to perturb their behavior in various ways by making them offers (ideally orthogonal ones) and observing their reactions.