We have to realize that were we to go to another planet, we would describe that planet with our own terminology and according to our own experience.  Whether or not our observations were "ancient-sounding" or "post-modern" would have to be interpreted by those reading our words.  If you read prophesies in the Book of Isaiah in the Bible, he describes horseless chariots as future modes of transportation.  Is he talking about our automobiles?  If so, he described them in his own way of understanding for the time period he lived in.  I think we would do the same if we were to see into the future or to visit another planet totally unlike our own. 

I really guess it would depend on the perspective of the alien.  Obviously its society has advanced technology or it wouldn't be able to get here.  Therefore, I imagine it would consider us a less advanced species technologically speaking.  Beyond that there is no frame of reference by which one could guess how they would describe us.

If they came here because they destroyed their own world they might consider us a very green and environmental society for the way we have "protected our planet", even though most "earthlings" think we have abused our home.  It all depends on perspective.

I think post 3 is right. A "post-modern alien" would cast doubt on his or her own ability to understand anything about the planet. They would categorize things differently, in ways humans wouldn't think of. Yet if they were truly post-modernists, they would also recognize the validity of earthlings' claims on their reality as much as their own. They would realize that things that don't make sense to them make sense to people on Earth, in other words, that there is not an objective reality. In fact, I think this question is an interesting thought experiment to get at the essence of post-modernism. (If such a thing as an "essence" exists, post-modernists would question whether it does).

One strategy would be to focus on language. 

The postmodernist is concerned with imprecision and unreliability of language and with epistemology, the study of what knowledge is.

An alien might come to earth and attempt to understand the planet by reading the literature of the planet, or just the dictionary. Looking up the word "earth" the alien may be surprised to see the this term has multiple meanings, refering to a planet and to a substance (soil/dirt).  

The dictionary offers a firm set of definitions for this term, but no single defintion, which leads to a sense of complexity. The complexities of perception are, in part, what post-modernism is all about. 

An alien would be unaware of classifications such as "post modern," and therefore would not attempt to describe Earth in any particular manner. The alien's report would be very factual and filled with concrete descriptions of observations made while studying this new world. If the alien was evaluating Earth as a possible location for an expansion into...