We literally only got two lines from him, and maybe 10 seconds of footage. Besides that tattoo's, the way he acted seems like it's pretty faithful to most of the Joker stories I've read.
That's quite a baseless assumption. There are a plethora of reasons why she would be in this movie; the idea that Waller would need her to help track the Joker, chief among them. Not quite sure where you are getting that from. I'm no Harley Quinn expert, but a quick Google Image search makes it clear that this is hardly the first time that she has been objectified as a character.
Again, not sure where you are getting this, seeing as this movie comes out in more than a year, and WB hasn't even started to market it.