I'm very puzzled!
1- It's impossible they killed Robin together and that they did it "recently" (2 years before "Suicide Squad" or so). That's because in BvS, Batman has already "changed" a lot of years before - turning into a ruthless and cruel vigilante.
My guess is that Joker killed Robin LONG TIME before he would meet Harleen at Arkham Asylum.
2- Had Batman just smashed Joker's teeth at that point? I mean, did Joker already get silver teeth in Harley Quinn's origin flashbacks? I remember so.
3- Are Joker's hair supposed to be green because the acid vat? It's not that much clear in the movie.
4- Are Harley's hair supposed to be half pink, half blue because the acid vat? Not clear, again.