Supposing SETI discovered real evidence of an intelligent extraterrestrial civilisation, say, less than ten light-years distant; two-way communication. although rather stilted, is a genuine possibility; you can ask questions and have a hope of seeing them answered in your own lifetime.
So, as a member of the worlds most intelligent message board, you are nominated to the committee that will compose intelligent questions to pose to these aliens; given that the contexts will largely be built upon those that can be described as universal (so maths, physics, chemistry, logic, etc), what sorts of questions would you hope to ask?
I would want to open with the idea of “Can we begin with a full exchange of scientific knowledge?”
I would send with the question, a lot of our Science Knowledge.
As jokes seem required, I would add, “Who do you think was the best Trek Captain?”
Serious answer: Send them something that can be decoded as the digits of Pi, e, or the Fibonacci sequence, then see if they respond with a similar pattern. I guess that would be the “establishing contact” part.
Then I’d ask “Do you die? And what do you think happens after death?”
Is it just you and us, or do you know of any other civilizations?
What are the basic chemical processes of life on your planet? Are you carbon-based with an oxygen-CO2 respiratory cycle, or something else?
What’s your anatomical structure? Are you vertebrates? (See enclosed anatomical diagrams showing differences between vertebrate and invertebrate lifeforms.)
Can you send us some samples of your art?
Just out of pure idle curiosity, can persons of your species be psychologically conditioned to perform menial tasks? And what’s your pain threshold?
If they had something similar in concept to religion. if so, tell us about their gods.
I’d ask if they had a dandelion problem.
Have they polluted their world? Even if they have found a clean, renewable energy source, there must be some loss to their planet from when they had to use dirty, non-renewable sources. Wouldn’t there?
If you guys have been around longer than we have – how much should we be worried about comets and asteroids hitting our planet? Is it really urgent for us to build some kind of heavenly-bodies defense system?