The statue of liberty is based off of 'Persephone' Goddess of the underworld, not sure that's who Hey-Zeus would be hanging with.
Hmmm, there's protocol when a salute is 'required' but you can pretty much salute anyone you want as long as they aren't a foreign power/adversary. My troops would salute me all the time, one of the younger officers bitched to my commander about it, turns out he thought it was awesome and noted my troops were pretty damn sharp at their jobs unlike others. I don't know 100% for sure, but I'm thinking, once you hold the title of Commander and Chief, you are always warranted a salute, but don't quote me on that.