1) Shuten are insisting on handling this themselves, though the Department of the Enma is sending Fire and Rescue, regardless. That being said, Azula will need time to actually get information from Fire and Rescue about what they discover during their attempts to put out the fire. She should probably be more focused on if there are bombs planted in Enma territory.

2) She doesn't strictly need to, since she has armory access, but if she finds something particularly cool, she can probably get away with sneaking away with it. She'll need to find a personal place to stash it, though, since it can't go back into the Enma's armory... legally, anyways.