The Heart of Lorkhan wasn't destroyed. The enchantments holding it in place and enableing one to draw power from it were.
It escaped. As well, God's body parts don't act like mortal's ones..Lorkhan's the "missing God", but he's out there somewhere "alive".
Tricksters don't die easy. Especially ones that are Gods.
I think Azura isn't the best Daedra. But in my book none of them are, really. They're all arbitary. Azura just like keeping up appearances. In the Pocket Guide (or the old one at least) the author writes a setence about each god.
But she still ain't good. She's more or less using you to tear apart the Dunmer's temple, which is a pretty big part of their life. And to get rid of would-be-gods.
She's using you to kill the Tribunal, who broke an oath sworn in her name, some wannabe God who wants to make everyone a god (Ur) AND collaspe the Dunmer temple so she can try to garner more worshipers for herself. And the whole "I helped the Nerevarine save the world" looks good for her.
