Yes, hence the idea that you can defeat god-like beings in Spirit Combat within a heroquest framework.
1. Yes. Any gods you meet will act according to their behaviour in the myths. Possibly this might not hold true if you meet a heroquester who has taken on the role of the god, but even in this case, acting out of character opens them up for an identity challenge.
2. I say no. The god world and the herorealms have a timeless quality to them, where you can encounter entities before they get destroyed. I don't think the Spirit World shares this quality. Wakboth in a heroworld heroquest, yes; in a spirit world quest, no.
3. This seems perfectly reasonable. Although most spirits act only in accordance to their natures as well.