U can go to options and check "enable skip mode" there. Then U can skip fights by clicking on "skip/win" (or something similar) in the bottom middle of the screen.
Mission "hero returns" -> "go back to lady". How is that possible? The way to the house right next to Carceburg is blocked (invisible wall). The only option is to fast travel to the HUB or directly to the forest. The HUB leads to the forest and the forest to the HUB and back to Carceburg.