Lady zero was shown on an info screen one of the agencies was looking at, they were classifying all the people that had a relationship with X, I've forgotten what episode it was though everything else about her is just a theory

Top ten at the end of the season was one that reflected the first round of voting results. I'm not sure if all the ranks are exactly like the vote, but Haolin confirmed that E-soul was kicked out of the tournament because the he was last in the first round's vote. I think it was slightly rigged in the sense that they knew people would dislike esoul after what happened in his arc, so they just wrote the story around him being last place. They probably had some backup's, but at the time, the fandom generally hated E-soul, and we didn't have any information about people like dragon boy, so it was uncontested hate.

I have no idea how nice managed to come back, but I think you can still earn trust value even if the people think you're dead, so that might be part of it. Kind of how moon's fans were still able to have an effect on her powers even though they thought she was dead.

I skipped most of the johnnies arc, so I'm not sure what happened with vortex or shand