The general rule is once you realize the error, inform the other player (don't hide anything), and if it can be practically undone, then it should be undone. Integrity is important because if you realize something a bit later and your opponent doesn't, and that "something" benefited you, you really need to inform the player of the error and work to make it right. Now the other player may opt to let it slide, since he missed it too, but at least he knows and has made his choice to let it slide. This really only applies to mandatory abilities, not optional (for example, you are not obligated to tell him he missed his Sheol trigger). But once you are aware of something that is mandatory, such as Confusion of Mind negating the rescuing heroes, inform that player of that and work to rectify it.
If it's something you become aware of well-after the fact, such as you or your opponent couldn't do something in the prep phase but unwittingly did anyway, and either you or he (or both) realized in the discard phase (after having a battle), or even next turn, it's probably too late by then because most likely many other things happened since then that would probably have to be reversed or were related to the original play in the prep phase. If it's something like you played Root of Jesse in prep phase that protected your meek heroes in battle but your opponent had Golden Calf active, and your meek heroes won due in part to the protection, and either of you realized in your discard phase the error, then that's something that may be too late. Or, you both could strike towards a compromise and say that the soul goes back to your opponent, and you and your opponent undo the battle, getting back heroes and evil characters, etc. and act as if the battle phase was skipped.
So more to your point with your scenarios, for scenario 1 & 2, if those actions can be practically undone then they should be. It's ultimately the responsibility of both players to be aware of the game state, cards that are in play and abilities that are active. If it's something, such as you have Coliseum out, and your opponent plays a CBN enhancement (not realizing it will get tossed), and you tell him it's tossed and he wants to take that back, the take back should not occur since it was the other player's responsibility to know what's in your territory before he plays it. It's a mistake he has to work through.
I hope this clarifies things for you.
