Any mercy for Diogenes on your part is folly; blind him. I support choice 3. He challenged you openly - others may try in the future if they think they may get away with it with possibilities for future attempt.

Send the empress to the Convent - effective and reasonable. She shall be removed from the political field, but you won't bring the ire of God (in the eyes of the people ) by mistreating your own mother. Choice 2.

As for the Armenian, you need to show that you're not a tyrant to the court; and he is powerless on his own. Banish him, to show that law and order still works in the empire, but that you are merciful in judgement. To let him get away with that freely defies legal justice, and therefore your own Imperial authority, even if it is an honourable choice. Choice 2: Exile.