I think I read some comments that the metal teeth Joker has is a result from a previous run in with Batman (where they all got knocked out).
Given this universe's Batman will already be a battle hardened hero, it's perhaps also might suggest that the Joker has been around for a while too?
Yes very good point. In TDKR, The Joker was 'awoken' by Batman's return. I wonder if he will appear (or be mentioned) in BvS.