Anabanana said:
what does the government plan on doing with the stone if the expedition succeeds and what are the character's thoughts on that possibility?
Again this is what your character thinks they will do:
Honestly they will probably add it to the treasury and just sit on it so to speak, for them it is less about what the stone can do and more about keeping it out of the hands of others. The emperor is an Archmage after all, he likes hording powerful things just like any other mage.
The character does not really want that to happen, but she is not a fool, the Imperials do provide advantages as outlined earlier, ideally she would like to keep it and unlock its secrets, largely just for the knowledge and power. Any motivation beyond that will have to come from the decisions you all make.
Half of the stone would give the user some power over the elements but it would be limited and fairly fragile sort of thing, I won't limit the amount of power you can try to draw from it but it may backfire as it is damaged.
Now the completed stone could flood cities, cause droughts, start fires through lightning, or level armies with powerful winds. It could also be used for good however, the war has left a lot of the eastern lands ruined, the stone could be used to improve soil quality in the Barrier (a 200 mile stretch of wasteland that runs from the city to the mountains in the west, caused by the magical fires Balor used to take the city), promote plant growth, fight wild fires, improve crop yields and help the empire recover, but the bureaucracy of the empire may or may not realize its potential if they get a hold of it.
On why it is illegal to enter the ruins:
Following Alric's successful occupation of the city a group of treasure hunters managed to wake up the ghost of an ancient Myrkridian Pack Mage (sort of like a big werewolf that knows magic and hates humans on principle). It killed about one hundred civilians, fifty legionaries, and six Heron Guards before the Heron Guards put it down. There are very dangerous things below the city, left over from the wars and even earlier. That is why it is illegal to go down there without a permit, you will have to be careful.