Search for ExtraTerrestrial Intelligences: haram?

Throughout the Quran man is invited and encouraged to study the heavens and the earth. Therefore studying the creation of God is absolutely necessary. Whether you are studying biology or astronomy like you mentioned, mankind is highly encouraged to pursue inquiry in the Allah�s creation and gain knowledge.

But it depends on what type of pursuit of knowledge is it. Is it based on a metaphysical perspective or a secular one? The points you mentioned would come from a secular mind, I believe and I will tell you why I think that.

In Islam Knowledge and humility live parallel to each other. Knowledge without humility leads towards arrogance. The following verses of the Quran were the first ones to be revealed in the chronology of revelation and they encourage reading, writing and learning but also warns of the result of a blind pursuit might lead mankind towards:

Al Quran 96:1-7

READ in the name of thy Sustainer, who has created (2) created man out of a germ-cell!2 (3) Read - for thy Sustainer is the Most Bountiful One (4) who has taught [man] the use of the pen (5) taught man what he did not know! Nay, verily, man becomes grossly overweening (7) whenever he believes himself to be selfsufficient: (8) for, behold, unto thy Sustainer all must return.

Blind pursuit of knowledge without any spirituality leads towards us towards creating concepts and ideas and results in ideologies that might be destructive for mankind. Therefore pursuit of knowledge of the entire creation is absolutely necessary but disconnecting the Creator can lead towards our own destruction.

So you speak all day everyday about the beautiful structure of a house, you praise and explain its architecture and its make, but you completely omit and to an extent even question the existence of the maker? That is what Islam forbids, following Verse of the Quran mentions this point:

Al Quran 36:77

IS MAN, then, not aware that it is We who create him out of a [mere] drop of sperm - whereupon, lo! he shows himself endowed with the power to think and to argue

Al Quran 36:78

And [now] he [argues about Us, and] thinks of Us in terms of comparison, and is oblivious of how he himself was created! [And so] he says, "Who could give life to bones that have crumbled to dust?

The power to think and to argue is great and needs to be put in to use, but never forget your own humble origin coming a drop of sperm and accountability that we will need to give as to how we made use of it in this earthly life.

Commenting on your questions, I would quote the following verse that might help you understand from a metaphysical Islamic perspective where do we stand when compared with entire creation of Allah:

Al Quran 33:72

Verily, We did offer the trust to the heavens, and the earth, and the mountains: but they refused to bear it because they were afraid of it. Yet man took it up

This word called �Amanah� which is translated as �Trust� means that mankind has been endowed with a potential so great that even the mountains, heavens and the earths and no other creation �can bear� meaning they all have been made subservient to us, given to us as a test to see how we make use of them.

We are the superior beings and all other creation is lesser. Us being superior does not mean we become arrogant but it is to recognize this fact so we become grateful. Our failure to be guided by a higher form of guidance (the revelation) is what keeps us from understanding our true potential.

God is testing us to see if we try to play gods or be in harmony with the rest of the creation of the Creator. As far as I can see, the technological advance, even though with all its positive points, is becoming a source of our gradual destruction such as the very imminent threat of world war 3 and even star wars between advanced nations like Russia, China, US and Western Countries.

Al Quran 30:41 

[Since they have become oblivious of God,] corruption has appeared on land and in the sea as an outcome of what men's hands have wrought: and so He will let them taste [the evil of] some of their doings, so that they might return (to the right path].