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 new territory for the lifeforms existing on the alien's home planet, the report would probably also include assessments of Earth in terms of compatibility with whatever uses the aliens were considering for the planet.
For example, the alien might describe climate changes on Earth by reporting, "Some parts of the planet experience wide variations in temperature at different times of the planet's rotation around it's star. Temperature changes may be accompanied by violent storms causing destruction of plant life and items constructed by the dominant animals of the planet. In areas having cold temperatures, the elemental compound H2O may fall onto the planet as cold white bits of matter that may accumulate to great depth; liquid masses of this compound may become solid in cold conditions. In areas having hot temperatures, the compound falls in a liquid form; when large amounts of the compound fall on a small area of the planet in a short period of time, the planet area may be severely damaged due to an incapability of the planet to absorb the compound quickly."
(Don't you need to know what the 'modern' alien thought in order to see things from the 'post modern' alien's perspective?) But, going with your idea, then I suppose the post-modern alien's view Earth would be based on the Alien's observation of its own emotional reactions...
'I felt blah blah blah about all the hunger and disease.'
'I really got blah blah blah about all the wars.'
'When I saw the Sistine Chapel I felt blah blah blah.'
'America made me want to blah blah blah.'