|Since we are not fighting against a military, who exactly are we attacking?
The two main "groups" of people that we are trying to fight over there are the insurgents and the terrorist groups like Al-queda in Iraq. Insurgent is just a fancy word for a person fighting against a government or some other authority. An insurgent is the same as a rebel or guerilla fighter (during Vietnam this would have been the Viet Cong) which more than qualifies them as military targets.
Unfortunately, there have been a few instances of soldiers or Marines committing crimes against Iraqi civilians. Most of them can probably be attributed to the frustration of trying to find an enemy that disappears into the civilian population but that doesn't excuse those who have committed the crimes, far from it.
A "shock and awe" campaign is a military strategy designed to rapidly erode or completely destroy and enemy's will to fight. This is not only done by intense bombing of military targets but also by disrupting the infrastructure of a country such as transportation (ie-bridges), communications, and power, etc. "Shock and awe" isn't a new phrase that was coined during Operation Iraqi Freedom. Sun Tzu, who wrote the book The Art of War over 2000 years ago, has been quoted as having used the phrase.
Sadly, as with any war, there will be civilian casualties as a result of such intensified bombing. All that can be done is to try is limit them as much as possible. Harlan K. Ullman, who wrote the "shock and awe" doctrine for the U.S. military in 1996 has said that he feels the U.S. scaled back from the original plan as it was intended because there were political concerns over civilian casualties. There is also debate as to whether or not the campaign had the desired effect on the Iraqi military. While many units gave up and many were also without any sort of organizational command, others were able to still put up stiff resistance. The bombing campaign from Desert Storm was much more effective in destroying the Iraqi army's will to fight, which I saw the after effects of first hand. IMHO, the entire operation was rushed and poorly planned.
This isn't quite the same as what occurred in World War II with the carpet bombing of entire cities to demoralize the enemy (population included). The "shock and awe" campaign wasn't targeting civilians per se, the infrastructure of Baghdad was the target, there were civilians that happened to be killed in the process, which is pretty much unavoidable. Laser guided bombs allow for more "precision" strikes but not all munitions used are "smart". Not all bombs will hit their intended targets.