With scenario # 1 how many outs? I think if there are less than two outs the error may not necessarily mean the run in unearned. If the ball that was hit was not thrown or the throw was clean, would the runner have advanced to home. If the runner would have stopped at third then it comes down to what happens after that play. If there were two outs then the run should be credited as unearned since you scored the play at first as a base hit regardless of the throw (ie. the batter, in your eyes would have beaten the throw to first.)
there is no such thing as mental error for score keepers. Your scoring is correct.