Why can she keep up with Batman in terms of fighting ?

But he is clearly crazy! You can't kill a crazy person.
Now excuse me while I count my totally wasn't a bribe money.

GOTHAM: It's Corrupt But It's Got One Hell Of A Economy So Fuck You Bludhaven

Gotham is in kinda-sorta-notreally-New York
Which has no death penalty

isn't Gotham canonically in New Jersey?

Ah, it is? NJ also lacks a death penalty, I'm pretty sure.

because it's just sex fighting for them

Stupid clown plot armor that surpasses stupid Bat plot armor.

Says who? Joker is crazy like Batman is over his parent's deaths. Joker aint crazy. Has shown at times that he is capable of thinking rationally. He is clearly faking it and the people of Gotham are retarded for not realizing.

I'm sure a state that had the Joker situation would reconsider that policy, even just as a temporary measure

That would be extremely unconstitutional.

didnt they have ivy buff her recently?

where did you hear that?