Technically in all parts of the state your supposed to get a fire permit which is good for a year. I don't really know why the state even does this, it's not like they teach you about fire safety when you get one. They just sign your name and send you on your way. I've never heard of anyone getting checked for it.
I've usually but not always been given a quick "don't do this" when I get my annual campfire permit. But even if they tell you nothing, the permit itself has some good fire safety info. AND, by having a permit you can't say you didn't know!
Using your stove is certainly allowed. I don't know if you need a permit for it but they can give you one when you get your wilderness permit.
Even for stove use you need the campfire permit. In some jurisdictions the wilderness permit is a campfire permit; I'm not sure about here because I get a campfire permit every year anyway.