It looks like a headline. As such it need not be perfectly correct grammatically, especially with regard to articles like "the". Nevertheless, unless someone received a part of the emperor from the empress (his head?), this does not make sense. "Emperor Parts from Empress" seems to be the intended headline.
you said "someone received a part of the emperor from the empress (his head?)". But "Emperor Part From Empress' seems referring to "the empress gave her organ to the emperor".
A 'placard' consists of a large piece of cardboard attached to a stick. There is usually a message written on the cardboard in capital letters.
In this instance, the placard would say EMPEROR PART FROM EMPRESS. 'Part from' is an imperative, meaning 'separate yourself from'. As with headlines, it's permissible to leave out 'the' and 'a' when writing placards.
Yes, you found another possible interpretation! In the case of headlines it is often possible to find many readings, especially if you're willing to consider extremely fanciful ones!