1. I dont think SMB3 is a stage play because the only evidence of (aside from Word of God) it are aesthetics, some of which were altered in remakes such as the All-Stars version. Other details such as Mario exiting stage right are present in other games so why does SMB3 in particular have to be a play?
Furthermore Super Mario Worlds (which is SMB4) manual directly references the events of SMB3 as something that happened. I feel Miyamoto May have came up with the idea later.
2. I am willing to except Paper Mario as some other universe, namely because the games arent even sure what they are. A normal world thats Paper? A world thats so Paper they dont know what 3d objects are? A world where they know theyre paper?
3. Rosalinas history is just screwed up and Nintendo doesnt care. She delegated to yet another princess now.
4. While I would have sung a different tune years ago Ill accept the Koopalings arent Bowsers children. Evidence to me shows that there was some discrepancy between how the Koopalings were localized to Americans vs what the Japanese thought.