The Ardian Empire having a nuclear weapons program - I see no reason why they couldn't have such a program especially as the program never completes, they never get a nuclear weapon and the program would get shut down when the war ends (this also can go some way to explaining how other nations developed their programs). The question I have to answer as the player responsible for Ach's actions is what prompts Ach to develop a nuclear weapon and then drop it. Dropping it is the simpler one to answer, the harder one is what prompts it - this is what an Ardian program is intended to do, an Ardian program helps explain the origins of the Ach program.
As far as the Princess goes this is an issue created by the fact that the Devaux family somehow are both the Imperial family of the Ardian Empire and now the Praetors of the Allied States of Ardia, her involvement is simply in recognition of that and it explains how Achkaerin becomes aware of Ardia's intentions and thus makes certain decisions.