As I understand those Schopenhauer’s quotes (and I’m clearly not alone), he says that we perceive only inner representations of what we assume to be the outside world (which is true), thus we cannot say anything definitive about the nature of that world beside the fact that we can observe causal relationships in our representations, which must reflect causality of said world, whatever that world might be. And that's in essence all we can say about it with certainty (again a true empirical observation).

Now, some people call those causal streams simply “causality,” some (e.g. shamans) call them “intent.” As it seems, and that Stanford Encyclopedia quote confirms it, Schopenhauer uses the term "will” (which may come from Christian culture, but that's just my speculation).

But this "will" has nothing to do with human volition -- our choice making as well as the universal indeterminism or randomness are part of, and already accounted for in, that overarching causal mechanism (see his concept of “will to life” which clearly does not talk about deliberate volition and also keep in mind that Schopenhauer’s ideas predate theories of quantum mechanics such as indeterminacy, and so on). I also fail to see where in those quotes Schopenhauer mentions deliberate (human or universal) willpower.

All in all, Schopenhauer's "will" is not the deliberate mental process associated with intentional choices and actions as you present it.