Is the value of democracy purely instrumental? To put it another way: if 'the republic' truly worked, would it be better than the misfiring democracies that we see in the world?

This is a hard one. If you think, as did Kant, for instance (see his fine essay, "What is Called 'Enlightenment'" or Mill (read "On LIberty") that there is a special non-instrumental value in being a free participant in a public sphere where ideas and views can enter into dialogue with one another, and that this opportunity is essential to being a flourishing person, not just a means to increasing GDP, then the value of democracy is non-instrumental. I, for one, believe this.

Many coutries of the world are populated by the descendents of aggressive invaders, but we do not hold these people responsible for the atrocities their descendents committed. For example, most reasonable people would not blame modern Americans for the genocide of the Native Americans. How many generations does this cleansing process take? Are a second generation of settlers whose parents took their homeland through violence already blameless?

It is probably useful to distinguish blame from responsibility. One may not be to blame for a set of actions taken by one's ancestors, but if one benefits from them, and another is harmed by them, one might still morally owe reparations. For example, suppose that my parents stole all of your parents' wealth, and left it to me, leaving you destitute. It wasn't my fault, and the harm wasn't done DIRECTLY to you, but there is still a strong case to be made that I am in possession of stolen goods that rightly belong to you, and that I owe you reparations. Now, the more distant the harms are from current circumstances, the harder it gets to assign particular benefits and injuries, and to sort out specific sequellae of ancient wrongs. But the more immediate cases, or those where, despite the passage of time the benefits and burdens remain clearly traceable, might well demand reparation, even if they don't demand guilt.