And they never have the ability to shoot anyone who isn't actively killing people?
Police never have the AUTHORITY to shoot anyone who isn't actively attempting to kill people. That's the important issue here: authority, not "ability." Without authority, the use of force is criminal.
You're mistaken. Arkansas cops recently opened up on a guy who was driving away from them, allegedly because because they soberly considered the situation and decided that the odds of him killing somebody were high, but probably because some rookie panicked and the vets decided riddling the dude was the popular thing to do; yet none of them has been charged with a crime. It's likely none will ever be charged with a crime. The wrongful death lawsuit from the driver's family is almost certainly gonna get thrown out by the Supremes.
The victim wasn't actively trying to kill anybody, he was actively trying to get the fuck away and in the process he was likely to kill somebody. His girlfriend/passenger was also totally innocent of intending to kill anybody. And due to the magic of prosecutorial discretion, even if the Supremes change their minds and rule the deaths were not justified nobody will ever go to jail for the crimes.
The second is simply false, because the authorities can shoot lots of people who aren't currently actively attacking anyone. You'll note that Federal troops...
Are you really too stupid to know the difference between police and the military?
Keep in mind that the military actually have fewer powers to use force on civilians then the police do. The posse comitatus act that allowed the KKK to drastically reduce the south's black population in the late 19th bans them from almost all law enforcement duties. But that act only applies within the 50 states.
As for powers to kill, they're quite similar. If you're in the military and you're not in a war-zone you don't get to shoot. Period. It doesn't really matter whether you hit your target, if you're on a base in Germany and you open fire on the local Imam you're going to Leavenworth. If you're in a war-zone you have to be able to prove you had some good reason to believe every shot you made wasn't heading towards some innocent person. It's generally easier to satisfy the brass that you had reason in the war-zone, because they wouldn't be giving you the extra pay if they didn't expect somebody to shoot at you, and they don't have the resources to investigate every single shell fired, but that doesn;t mean the legal theory is any different.
Now we've got many fewer enemies, and the process for finding them is much more complicated because they don't all wear the same shirt, but that just means that there's a lot of internal process the Executive branch has to go through before OKing the target.
The government also has to abide by the Geneva Conventions. Either the target is an enemy soldier and the Geneva Conventions apply, or he is not a soldier and US criminal law (including the 5th Amendment) applies. There is no other category. Obama (and GW Bush before him) might have claimed there was, but both of them are war criminals.
Dude,a treaty? Seriously?
Without an enforcement mechanism a treaty is a press release. This is because treaties are agreements between sovereign states, and sovereign states are allowed to do anything they want. That's the definition of sovereign. For example, they can re-define words. If Obama decrees Al Awlaki is an enemy combatant, because American English the name "Al Awlaki" has always been a synonym for "enemy combatant," it doesn't matter that that's ridiculous BS. Under international law, as Head of State of a Sovereign nation, he can do that, and the only people who can argue the point are other sovereigns (ie: countries), and they only get to do the contesting via the enforcement mechanisms in the treaty.
The enforcement mechanism of the Geneva Convention is nothing. Seriously. There is no Geneva Treaty Commission that can issue valid arrest warrants in the US. There is no automatic penalty on international money transfers, or guy who can order the Koreans to throw the Seventh Army out. Geneva gets obeyed not because it's a strong source of law, but because if we didn't obey it the Russians wouldn't either; which would mean our people get tortured. And the Russians, Chinese, etc. are not likely to risk their boys getting tortured by us to protect an Islamist preacher who probably wants to send Jihadists to their countries.