Obviously Arnold can control his invisibility, but the Arnold thing wasn't serious, so I'll skip that.As for the Talos, the letter says he wants to see the player develop his/her talents because Skyrim needs a true hero, maybe such as himself when he was alive. Also a God caring enough to play an active role isn't something that hasn't happened before, hell Tiber Septim himself manifested himself as an Imperial named Wulf and gave you an item to help you kill Dagoth Ur in Morrowind. It isn't unlikely that he would intervene again to stop the Aludin crisis. As for the war thing, like you said, maybe no matter who wins the war you'll be set up as the person who will unite the Empire again.As for the Greybeards, there isn't any good reason as to why they aren't it except the whole telling you where two words of power are at the same time. Even if this was some "test", cause we all know how telling you where words are via letter instead of directly to you tests your abilities to the max, they continue the letters and directly telling you where the words are throughout the main quest and after.