The people who did all those things are not "Egyptians," the people of the Pharaohs. They are Arabs, the people who occupied Egypt, marginalized its native Cushitic people, and overlaid their civilization with the Islamic branch of Mesopotamian civilization. The armies of Caliph Omar destroyed one of the world's six precious and unique civilizations, just as the armies of Europe destroyed that of the Olmec/Maya/Aztec and that of the Inca, overlaying them with the Christian Greco-Roman branch of Mesopotamian civilization and marginalizing their people.
You seem to generalize Islamic and Christian based conquests, and wrongfully compress them into one category. Spanish colonialism into the Americas, and their treatment/annihilation of the then present Aztecs/Maya/Incas is substantially different from the Caliphate’s growth from inner Arabia to Egypt (the West) and Persia (the North). As you erroneously imply, Omar’s conquests never directly lead to the destruction of the Egyptian civilization or extinction of any languages present there. The Egyptian civilization (prior to Omar) was always subject to change, and its deterioration was only a natural evolution (recall, Egypt had been in a stagnant and declining state for many years before Abu Bakr/Omar). A new lifestyle and language was introduced to the Egyptians, who readily accepted it because it was a stronger force to be part of. Languages aren’t erased by killing every speaker of it, until it’s lost completely. Introducing a more popular language that is part of a more powerful empire will naturally attract people towards it anyway. How do you think the Native American languages of today are being forever forgotten?
Thanks to the armies of Islam and Christianity, half of the world's irreplaceable civilizations are lost to us forever. These are the greatest atrocities that have ever been perpetrated by human beings. (I give a modicum of credit to the Arabs for not destroying all traces of Egyptian civilization: the Christians actually melted down the art of the New World peoples. But to say Omar's armies were slightly less evil than those who conquered the New World is, I hope, a perfect example of damning with faint praise.)
What civilizations did the Muslim (Arab) armies remove from history (preferably by Omar)? Staying on the topic of Omar, he actually aided the construction of many (aforementioned) cities. Atop of this, Omar did not loot/burn to the ground the cities he captured. Rather, he lived amongst them, building libraries and vital infrastructure that are still admired today. Considering this digression of topic occurred on the basis of Omar, I will focus more steadily on him. Unless I have accidentally skipped a few pages when reading my old history books, I cannot recall a time where a civilization was erased at the hands of Omar. The Omar I’ve read was the founder of cities, and an integral catalyst in the progression of civilization from the tribal men of Africa to the desert nomads of Arabia.
To steer this discussion back onto firmer linguistic ground, a "warrior" is a person who dedicates his life to defending people who cannot defend themselves--his own people or others in need. A warrior is not driven by vanity and does not conquer other peoples in order to inflate his image.
This is where you are mistaken. Contrary to your beliefs, a warrior is not someone who dedicates his life to defending the helpless, as you put it. A warrior, as defined by any dictionary (and as defined in regular dialogue) is a person well engaged/experienced in warfare; someone who has shown great vigor in battle. Keeping in mind these specific qualities of a warrior (based off dictionary descriptions), it is safe to say that Omar was deservingly a warrior. Conquering other people to inflate his own image was not of Omar’s principles, which is evident through his lifestyle and wartime policies. Did Omar steal all of Persia’s wealth and live lavishly like a King? Did he round of the civilians of the conquered regions and use them for pincushions? I’m afraid (for you) that the answer to both questions is “no”.
Alexander, like Abraham Lincoln, was perhaps originally motivated by a desire to protect the nation he served by strengthening it, but they both ended up debased by hubris, solidifying and/or expanding their empires by dishonorable means in order to earn a place in the history books. Genghis Khan was a megalomaniac and a textbook example of a sociopath who was obsessed with glory. He killed at least ten percent of the civilian populations he came in contact with for no other reason than his own vanity. This puts him in a class with Hitler: unpardonably despicable vermin, blots on the history of our species.
Of course all of these historical figures were obsessed with glory to varying degrees, and all likely committed some sort of atrocity (as perceived today) throughout their lifetime. Who could disagree to that? Certainly not me. However, we must give credit where it is due: these were some of the most influential, skilled, and powerful men in history, whose actions have helped shape civilization as we know it today. Despite their wrongdoings (however abundant), credence and some sort of appreciation/admiration must be given. It would be a crime to hold their unworldly achievements in contempt due to your abnormal hatred of them.
In America we are developing a tradition of letting the names of outrageous villains fall into obscurity, denying them what they strove for: a place in our memory. After a contemporary rock star took the surname of a California cult murderer, a practice was begun of referring to more recent mass murderers only as the Oklahoma City Bomber and the Beltway Snipers. It's a long shot, but perhaps the knowledge that one's name will not be remembered will reduce the motivation for high-profile crimes.
Then it becomes a battle of what crowd you are attempting to appease. If you refuse to offer media attention in vast portions to events like the Oklahoma City Bombing, then you’re likely to face loud controversy. Another example is the mall massacre that just recently happened: if you don’t feed that event the publicity it warrants, then there will be complaints in mass numbers, exclaiming that it deserves attention to raise awareness. They will argue that ignoring the event will make people turn a blind eye toward issues like necessary mall security, which in turn will lead to more events of the like.
In that trend, perhaps the Nazi leader should only be known as the Master of the Holocaust. As for the Mongol butchers, I get great joy from the fact that the patient Chinese people simply lulled them into decadence and absorbed them without violence. He is forgotten in the best possible way: What little he achieved has been erased, at least within that country.
The Chinese, in my opinion, turned out to be very lucky. Genghis Khan obliterated their Northern regions with unexpected ease, and stole all their treasure and material of value. If it wasn’t for the Mongol Empire’s lack of culturally-binding capabilities, China could (and most likely would) have faced much longer repercussions. The Mongols were weakened to withdrawal not by the Chinese, but by the Middle Eastern and Indian armies predominately (see Mamluks, generals such as Zafar Khan, battle of Ain Jalut). China seized advantage of Mongol misfortune that happened thousands of miles away.
Peace and harmony are the cornerstones of civilization. Anyone who kills and destroys is, by definition, not civilized, unless in self-defense against a direct threat from someone else who became uncivilized first.
Civilization, in order to advance, needs conflict, as history will show. It is small wonder why progression in all fields of knowledge occur during or immediately after some sort of conflict or conquest. Ultimately, you cannot view historical events (especially those which occurred 1400+ years ago) with the modern eye. What is deemed impermissible and uncivilized today may very well have been the exact opposite a millennium ago, which is why it is unfair to judge such actions by today’s laws and moral codes. The aftermath of Omar’s actions are well-documented and publicly recognized to be much more beneficial than harmful; they are acknowledged to have been prime advancers of Middle Eastern and African civilization, not destroyers of.