[Snape Is Draco's Godfather?]
The author was very curious—why did so many readers assume Snape was Draco's godfather? It was never mentioned in the original books; it was merely a common fanfiction setting. But didn't anyone find this setting unreasonable? Or did everyone misunderstand what a godfather was?
Sirius Black was indeed Harry's godfather in the original books, but Sirius Black and James were brothers-in-arms who would entrust their lives to each other, closer even than blood brothers. James's refusal to let Dumbledore be the Secret-Keeper in favor of Sirius Black made that clear enough.
Did anyone really think Lucius and Snape had that kind of life-and-death bond? At most, they were on fairly good personal terms, weren't they? The author truly could not imagine Lucius entrusting his son to Snape.
A godfather had the responsibility to set a good example and guide a child's growth. If Snape had been Draco's godfather, then he had unquestionably failed in that duty. Draco displayed so much childish behavior at school, yet Snape had never criticized or corrected him even once.
[The Trace Is on the Wand]
This, too, did not come from the original books, but was a common fanfiction setting.
The author found it quite unreasonable.
If the Trace were on the wand, then how could there have been the plot where Dobby framed Harry? If the Ministry of Magic monitored wands, shouldn't it have been able to tell that Harry's wand had not cast any magic?
The Trace was only introduced in the seventh book, so it was very likely that, early on, the Trace was merely a vague concept in Rowling's mind, without any detailed treatment. She did not attempt to refine the concept until the seventh book.
Refer to Chapter 13 of the sixth book. The original text