1. Yes---as others have said, how Ziegfeld throws around his money to the 'little person'...as well as just the rather 'meet cute' way he tried to convince her to sign with him. Flowers! A note! Let's do this thing! And it didn't seem like business, just a comical rivalry with the competitor.
2. Like the majority of early musicals (before "Show Boat" as an example), the song she sings doesn't move the plot along or explain the character--- it was Anna Held's signature song.
3. I don't know, given the period it reflects, that pre-code would have impacted it. Maybe a gratuitous undress