From what I remember, Hush was originally going to be the villain in The Batman. Then Matt decided to go with Riddler instead, because the story he wanted to tell fit his character best.
It would be a strange and unnecessary move to make Riddler the son of Edward Elliot. I also still see no similarities between Riddler and Hush. Riddler’s mother died in Arkham when he was an orphaned toddler. I’m assuming she gave birth to him in Arkham. His inspirations come from his own character history, the Zodiac Killer, Se7en and Michael Myers for sure.
Hush is way more flexible. His origin is already reimagined and Matt can use entirely different inspirations to really make him stand out even more. Matt should definitely lean heavily into his killer surgeon M.O.
Tommy and Bruce won’t be childhood friends due to Bruce being reclusive. Tommy was never an orphan either and I don’t expect him to be in this version. What may happen is that Bruce reaches out to Tommy after the revelation of Edward’s murder. From there it becomes more of a “keep your enemies close” sort of story line.