Watch the actual Inferno Cop series before you worry about shit like that. Even I didn't watch those. As educational as I'm sure they are, I know everything about Inferno Cop and his greatness already.
The second one is by the same God. I like them both around equally. It'll probably grow on you even more. Mai's dog is the only one that can troll Mai.
Also they should have used the first opening throughout the whole show. The 2nd one is growing on me, but the first is so epic.
I just got done with the episode where Mio is trying to draw her manga with everyone helping her. Oh man, her freaking out at the end was one of the best i've seen in an anime lol.
And Mai's dog definitely fits her personality for some reason.